This paper provides a compressive sensing (CS) method of denoising images using Bayesian
framework. Some images, for example like magnetic resonance images (MRI) are usually very
weak due to the presence of noise and due to the weak nature of the signal itself. So denoising
boosts the true signal strength. Under Bayesian framework, we have used two different priors:
sparsity and clusterdness in an image data as prior information to remove noise. Therefore, it is
named as clustered compressive sensing based denoising (CCSD). After developing the
Bayesian framework, we applied our method on synthetic data, Shepp-logan phantom and
sequences of fMRI images. The results show that applying the CCSD give better results than
using only the conventional compressive sensing (CS) methods in terms of Peak Signal to Noise
Ratio (PSNR) and Mean Square Error (MSE). In addition, we showed that this algorithm could
have some advantages over the state-of-the-art methods like Block-Matching and 3D
Filtering (BM3D).
Many algorithms have been developed to find sparse representation over redundant dictionaries or
transform. This paper presents a novel method on compressive sensing (CS)-based image compression
using sparse basis on CDF9/7 wavelet transform. The measurement matrix is applied to the three levels of
wavelet transform coefficients of the input image for compressive sampling. We have used three different
measurement matrix as Gaussian matrix, Bernoulli measurement matrix and random orthogonal matrix.
The orthogonal matching pursuit (OMP) and Basis Pursuit (BP) are applied to reconstruct each level of
wavelet transform separately. Experimental results demonstrate that the proposed method given better
quality of compressed image than existing methods in terms of proposed image quality evaluation indexes
and other objective (PSNR/UIQI/SSIM) measurements.
This document discusses dimensionality reduction techniques for hyperspectral images. It proposes using k-means clustering based on statistical measures like variance, standard deviation, and mean absolute deviation to select bands from hyperspectral images. The number of bands is first estimated using virtual dimensionality. Bands are then clustered based on their statistical properties and one band is selected from each cluster with the maximum value of the statistical measure. Finally, endmembers are extracted from the selected bands using N-FINDR.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
This document summarizes a paper that analyzes compressive sampling (CS) for compressing and reconstructing electrocardiogram (ECG) signals using l1 minimization algorithms. It proposes remodeling the linear program problem into a second order cone program to improve performance metrics like percent root-mean-squared difference, compression ratio, and signal-to-noise ratio when reconstructing ECG signals from the PhysioNet database. The paper provides an overview of CS theory and l1 minimization algorithms, describes the proposed approach of using quadratic constraints, and defines performance metrics for analyzing reconstructed ECG signals.
Spectroscopy or hyperspectral imaging consists in the acquisition, analysis, and extraction of the spectral information measured on a specific region or object using an airborne or satellite device. Hyperspectral imaging has become an active field of research recently. One way of analysing such data is through clustering. However, due to the high dimensionality of the data and the small distance between the different material signatures, clustering such a data is a challenging task.In this paper, we empirically compared five clustering techniques in different hyperspectral data sets. The considered clustering techniques are K-means, K-medoids, fuzzy Cmeans, hierarchical, and density-based spatial clustering of applications with noise. Four data sets are used to achieve this purpose which is Botswana, Kennedy space centre, Pavia, and Pavia University. Beside the accuracy, we adopted four more similarity measures: Rand statistics, Jaccard coefficient, Fowlkes-Mallows index, and Hubert index. According to accuracy, we found that fuzzy C-means clustering is doing better on Botswana and Pavia data sets, K-means and K-medoids are giving better results on Kennedy space centre data set, and for Pavia University the hierarchical clustering is better
This document presents a scalable method for image classification using sparse coding and dictionary learning. It proposes parallelizing the computation of image similarity for faster recognition. Specifically, it distributes the task of measuring similarity between images among multiple cores in a cluster. Experimental results on a face recognition dataset show nearly linear speedup when balancing the dataset size and number of nodes. Reconstruction errors are used as a similarity measure, with dictionaries learned using K-SVD for each image. The proposed parallel method distributes this similarity computation process to achieve faster image classification.
Effect of grid adaptive interpolation over depth imagescsandit
A suitable interpolation method is essential to keep the noise level minimum along with the timedelay.
In recent years, many different interpolation filters have been developed for instance
H.264-6 tap filter, and AVS- 4 tap filter. This work demonstrates the effects of a four-tap lowpass
tap filter (Grid-adaptive filter) on a hole-filled depth image. This paper provides (i) a
general form of uniform interpolations for both integer and sub-pixel locations in terms of the
sampling interval and filter length, and (ii) compares the effect of different finite impulse
response filters on a depth-image. Furthermore, the author proposed and investigated an
integrated Grid-adaptive filter, that implement hole-filling and interpolation concurrently,
causes reduction in time-delay noticeably along with high PSNR .
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
Many algorithms have been developed to find sparse representation over redundant dictionaries or
transform. This paper presents a novel method on compressive sensing (CS)-based image compression
using sparse basis on CDF9/7 wavelet transform. The measurement matrix is applied to the three levels of
wavelet transform coefficients of the input image for compressive sampling. We have used three different
measurement matrix as Gaussian matrix, Bernoulli measurement matrix and random orthogonal matrix.
The orthogonal matching pursuit (OMP) and Basis Pursuit (BP) are applied to reconstruct each level of
wavelet transform separately. Experimental results demonstrate that the proposed method given better
quality of compressed image than existing methods in terms of proposed image quality evaluation indexes
and other objective (PSNR/UIQI/SSIM) measurements.
This document discusses dimensionality reduction techniques for hyperspectral images. It proposes using k-means clustering based on statistical measures like variance, standard deviation, and mean absolute deviation to select bands from hyperspectral images. The number of bands is first estimated using virtual dimensionality. Bands are then clustered based on their statistical properties and one band is selected from each cluster with the maximum value of the statistical measure. Finally, endmembers are extracted from the selected bands using N-FINDR.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
This document summarizes a paper that analyzes compressive sampling (CS) for compressing and reconstructing electrocardiogram (ECG) signals using l1 minimization algorithms. It proposes remodeling the linear program problem into a second order cone program to improve performance metrics like percent root-mean-squared difference, compression ratio, and signal-to-noise ratio when reconstructing ECG signals from the PhysioNet database. The paper provides an overview of CS theory and l1 minimization algorithms, describes the proposed approach of using quadratic constraints, and defines performance metrics for analyzing reconstructed ECG signals.
Spectroscopy or hyperspectral imaging consists in the acquisition, analysis, and extraction of the spectral information measured on a specific region or object using an airborne or satellite device. Hyperspectral imaging has become an active field of research recently. One way of analysing such data is through clustering. However, due to the high dimensionality of the data and the small distance between the different material signatures, clustering such a data is a challenging task.In this paper, we empirically compared five clustering techniques in different hyperspectral data sets. The considered clustering techniques are K-means, K-medoids, fuzzy Cmeans, hierarchical, and density-based spatial clustering of applications with noise. Four data sets are used to achieve this purpose which is Botswana, Kennedy space centre, Pavia, and Pavia University. Beside the accuracy, we adopted four more similarity measures: Rand statistics, Jaccard coefficient, Fowlkes-Mallows index, and Hubert index. According to accuracy, we found that fuzzy C-means clustering is doing better on Botswana and Pavia data sets, K-means and K-medoids are giving better results on Kennedy space centre data set, and for Pavia University the hierarchical clustering is better
This document presents a scalable method for image classification using sparse coding and dictionary learning. It proposes parallelizing the computation of image similarity for faster recognition. Specifically, it distributes the task of measuring similarity between images among multiple cores in a cluster. Experimental results on a face recognition dataset show nearly linear speedup when balancing the dataset size and number of nodes. Reconstruction errors are used as a similarity measure, with dictionaries learned using K-SVD for each image. The proposed parallel method distributes this similarity computation process to achieve faster image classification.
Effect of grid adaptive interpolation over depth imagescsandit
A suitable interpolation method is essential to keep the noise level minimum along with the timedelay.
In recent years, many different interpolation filters have been developed for instance
H.264-6 tap filter, and AVS- 4 tap filter. This work demonstrates the effects of a four-tap lowpass
tap filter (Grid-adaptive filter) on a hole-filled depth image. This paper provides (i) a
general form of uniform interpolations for both integer and sub-pixel locations in terms of the
sampling interval and filter length, and (ii) compares the effect of different finite impulse
response filters on a depth-image. Furthermore, the author proposed and investigated an
integrated Grid-adaptive filter, that implement hole-filling and interpolation concurrently,
causes reduction in time-delay noticeably along with high PSNR .
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
This paper proposes a new algorithm for single-image super-resolution that exploits image compressibility in the wavelet domain using compressed sensing theory. The algorithm incorporates the downsampling low-pass filter into the measurement matrix to decrease coherence between the wavelet basis and sampling basis, allowing use of wavelets. It then uses a greedy algorithm to solve for sparse wavelet coefficients representing the high-resolution image. Results show improved performance over existing super-resolution approaches without requiring training data.
A COMPARATIVE STUDY ON DISTANCE MEASURING APPROACHES FOR CLUSTERINGIJORCS
Clustering plays a vital role in the various areas of research like Data Mining, Image Retrieval, Bio-computing and many a lot. Distance measure plays an important role in clustering data points. Choosing the right distance measure for a given dataset is a biggest challenge. In this paper, we study various distance measures and their effect on different clustering. This paper surveys existing distance measures for clustering and present a comparison between them based on application domain, efficiency, benefits and drawbacks. This comparison helps the researchers to take quick decision about which distance measure to use for clustering. We conclude this work by identifying trends and challenges of research and development towards clustering.
Review of Use of Nonlocal Spectral – Spatial Structured Sparse Representation...IJERA Editor
This document summarizes a research paper that proposes a new method for hyperspectral image restoration using nonlocal spectral-spatial structured sparse representation. The key points are:
1) It introduces using nonlocal similarity and spectral-spatial structure of hyperspectral images in sparse representation models. Nonlocal similarity means similar image patches can be represented by shared dictionary atoms, distinguishing true signals from noise.
2) Using 3D blocks that exploit spectral and spatial correlations, rather than 2D patches, for sparse coding. This better distinguishes true signals and noise.
3) A mixed Poisson-Gaussian noise model is used to handle signal-dependent and signal-independent noise present in hyperspectral images. Variance-fitting transformation
Web image annotation by diffusion maps manifold learning algorithmijfcstjournal
Automatic image annotation is one of the most challenging problems in machine vision areas. The goal of this task is to predict number of keywords automatically for images captured in real data. Many methods are based on visual features in order to calculate similarities between image samples. But the computation cost of these approaches is very high. These methods require many training samples to be stored in memory. To lessen thisburden, a number of techniques have been developed to reduce the number
of features in a dataset. Manifold learning is a popular approach to nonlinear dimensionality reduction. In
this paper, we investigate Diffusion maps manifold learning method for webimage auto-annotation task.Diffusion maps
manifold learning method isused to reduce the dimension of some visual features. Extensive experiments and analysis onNUS-WIDE-LITE web image dataset with
different visual featuresshow how this manifold learning dimensionality reduction method can be applied effectively to image annotation.
Computer apparition plays the most important role in human perception, which is limited to only the visual band of the electromagnetic spectrum. The need for Radar imaging systems, to recover some sources that
are not within human visual band, is raised. This paper present new algorithm for Synthetic Aperture Radar (SAR) images segmentation based on thresholding technique. Entropy based image thresholding has
received sustainable interest in recent years. It is an important concept in the area of image processing.
Pal (1996) proposed a cross entropy thresholding method based on Gaussian distribution for bi-modal images. Our method is derived from Pal method that segment images using cross entropy thresholding based on Gamma distribution and can handle bi-modal and multimodal images. Our method is tested using
Synthetic Aperture Radar (SAR) images and it gave good results for bi-modal and multimodal images. The
results obtained are encouraging.
This document provides an overview of digital image processing. It discusses what image processing entails, including enhancing images, extracting information, and pattern recognition. It also describes various image processing techniques such as radiometric and geometric correction, image enhancement, classification, and accuracy assessment. Radiometric correction aims to reduce noise from sources like the atmosphere, sensors, and terrain. Geometric correction geometrically registers images. Image enhancement improves interpretability. Classification categorizes pixels. The document outlines both supervised and unsupervised classification methods.
This document presents research on content-based image retrieval using color and texture features. It proposes using both quadratic distance based on color histograms to measure color similarity, and pyramid structure wavelet transforms and gray level co-occurrence matrix (GLCM) to measure texture. For color features, quadratic distance is calculated between color histograms to retrieve similar images based on color. For texture, pyramid structure wavelet transforms are used to decompose images into sub-bands and calculate energy levels, while GLCM extracts texture statistics. The methods are evaluated on a dataset of 10000 images and results show the integrated approach of color and texture features provides more accurate and faster retrieval compared to individual features.
Hyperspectral image mixed noise reduction based on improved k svd algorithmeSAT Publishing House
This document summarizes a proposed algorithm for reducing mixed noise in hyperspectral imagery. Hyperspectral images capture information across the electromagnetic spectrum and can be represented as three-dimensional tensors. The proposed method uses tensor decomposition and an improved K-SVD algorithm to adaptively detect and remove Gaussian noise, impulse noise, and mixtures of these from hyperspectral data. It formulates the noise removal problem using a weighted regularization approach and solves related optimization problems using techniques like singular value decomposition. The goal is to separate noise and noise-free components to reconstruct a cleaned hyperspectral image tensor.
This summarizes a research paper that proposes a new approach for noise estimation on images. It uses wavelet transform because of its sparse nature, then applies a Bayesian approach by imposing a Gaussian distribution on transformed pixels. It checks image quality before noise estimation using maximum likelihood decision criteria. Then designs a new bound-based estimation process using ideas from Cramer-Rao lower bound for signals in additive white Gaussian noise. The experimental results show visually better output after reconstructing the original image.
Boosting ced using robust orientation estimationijma
In this paper, Coherence Enhancement Diffusion (CED) is boosted feeding external orientation using new
robust orientation estimation. In CED, proper scale selection is very important as the gradient vector at
that scale reflects the orientation of local ridge. For this purpose a new scheme is proposed in which pre
calculated orientation, by using local and integration scales. From the experiments it is found the proposed
scheme is working much better in noisy environment as compared to the traditional Coherence
Enhancement Diffusion
Comparative Study of Compressive Sensing Techniques For Image EnhancementCSCJournals
Compressive Sensing is a new way of sampling signals at a sub-Nyquist rate. For many signals, this revolutionary technology strongly relies on the sparsity of the signal and incoherency between sensing basis and representation basis. In this work, compressed sensing method is proposed to reduce the noise of the image signal. Noise reduction and image reconstruction are formulated in the theoretical framework of compressed sensing using Basis Pursuit de-noising (BPDN) and Compressive Sampling Matching Pursuit (CoSaMP) algorithm when random measurement matrix is utilized to acquire the data. Ultimately, it is demonstrated that the proposed methods can't perfectly recover the image signal. Therefore, we have used a complementary approach for enhancing the performance of CS recovery with non-sparse signals. In this work, we have used a new designed CS recovery framework, called De-noising-based Approximate Message Passing (D-AMP). This method uses a de-noising algorithm to recover signals from compressive measurements. For de-noising purpose the Non-Local Means (NLM), Bayesian Least Squares Gaussian Scale Mixtures (BLS-GSM) and Block Matching 3D collaborative have been used. Also, in this work, we have evaluated the performance of our proposed image enhancement methods using the quality measure peak signal-to-noise ratio (PSNR).
Wavelet-Based Warping Technique for Mobile Devicescsandit
The document proposes a wavelet-based warping technique to render novel views of compressed images on mobile devices. It uses Haar wavelet transform to compress large reference and depth images, reducing their size. The technique decomposes the images into approximation and detail parts, but only uses the approximation parts for warping. This improves rendering speed on mobile devices. The framework is implemented using Android tools and experiments show it provides faster rendering times for large images compared to direct warping without compression.
Image compression by ezw combining huffman and arithmetic encoderIAEME Publication
This document summarizes an article that proposes combining Embedded Zero tree Wavelet (EZW) image compression with Huffman and arithmetic encoders to achieve additional compression. EZW is an effective wavelet-based image compression algorithm that encodes coefficients in order of importance. The paper argues that applying Huffman coding followed by arithmetic encoding to the output of an EZW compressor provides around 15% extra compression with minimal quality loss. It describes the EZW encoding process, including the concept of zero trees that allows efficient coding of significance maps, and how discrete wavelet transforms decompose images into frequency subbands.
IMAGE SEGMENTATION BY USING THRESHOLDING TECHNIQUES FOR MEDICAL IMAGEScseij
Image binarization is the process of separation of pixel values into two groups, black as background and
white as foreground. Thresholding can be categorized into global thresholding and local thresholding. This
paper describes a locally adaptive thresholding technique that removes background by using local mean
and standard deviation. Most common and simplest approach to segment an image is using thresholding.
In this work we present an efficient implementation for threshoding and give a detailed comparison of
Niblack and sauvola local thresholding algorithm. Niblack and sauvola thresholding algorithm is
implemented on medical images. The quality of segmented image is measured by statistical parameters:
Jaccard Similarity Coefficient, Peak Signal to Noise Ratio (PSNR).
A Quantitative Comparative Study of Analytical and Iterative Reconstruction T...CSCJournals
A special image restoration problem is the reconstruction of image from projections – a problem of immense importance in medical imaging, computed tomography and non-destructive testing of objects. This is a problem where a two – dimensional (or higher) object is reconstructed from several one –dimensional projections [1]. The reconstruction techniques are broadly classified into three categories, analytical, iterative, and statistical [2]. The comparative study among these is of great importance in the field of medical imaging. This paper aims at comparative study by analyzing quantitatively the quality of image reconstructed by analytical and iterative techniques. Projections (parallel beam type) for the reconstruction are calculated analytically by defining Shepp logan phantom head model with coverage angle ranging from 0 to ±180o with rotational increment of 2o to 10o. For iterative reconstruction coverage angle of ±90o, iteration up to 10 is used. The original image is grayscale image of size 128 X 128. The Image quality of the reconstructed image is measured by six quality measurement parameters. In this paper as analytical technique; simple back projection and filtered back projection are implemented, while as iterative; algebraic reconstruction technique is implemented. Experiment result reveals that quality of reconstructed image increase as coverage angle, and number of views increases. The processing time is one major deciding component for reconstruction. Keywords: Reconstruction algorithm, Simple-Back projection algorithm (SBP), Filter-Back projection algorithm (FBP), Algebraic Reconstruction Technique algorithm (ART), Image quality, coverage angle, Computed tomography (CT).
Improved probabilistic distance based locality preserving projections method ...IJECEIAES
In this paper, a dimensionality reduction is achieved in large datasets using the proposed distance based Non-integer Matrix Factorization (NMF) technique, which is intended to solve the data dimensionality problem. Here, NMF and distance measurement aim to resolve the non-orthogonality problem due to increased dataset dimensionality. It initially partitions the datasets, organizes them into a defined geometric structure and it avoids capturing the dataset structure through a distance based similarity measurement. The proposed method is designed to fit the dynamic datasets and it includes the intrinsic structure using data geometry. Therefore, the complexity of data is further avoided using an Improved Distance based Locality Preserving Projection. The proposed method is evaluated against existing methods in terms of accuracy, average accuracy, mutual information and average mutual information.
Satellite image Compression reduces redundancy in data representation in order to achieve saving in the
cost of storage and transmission image compression compensates for the limited on-board resources, in
terms of mass memory and downlink bandwidth and thus it provides a solution to the (bandwidth vs. data
volume) dilemma of modern spacecraft Thus compression is very important feature in payload image
processing units of many satellites, In this paper, an improvement of the quantization step of the input
vectors has been proposed. The k-nearest neighbour (KNN) algorithm was used on each axis. The three
classifications considered as three independent sources of information, are combined in the framework of
the evidence theory the best code vector is then selected. After Huffman schemes is applied for encoding
and decoding.
An efficient fusion based up sampling technique for restoration of spatially ...ijitjournal
The various up-sampling techniques available in the literature produce blurring artifacts in the upsampled,
high resolution images. In order to overcome this problem effectively, an image fusion based interpolation technique is proposed here to restore the high frequency information. The Discrete Cosine Transform interpolation technique preserves low frequency information whereas Discrete Sine Transform preserves high frequency information. Therefore, by fusing the DCT and DST based up-sampled images, more high frequency, relevant information of both the up-sampled images can be preserved in the restored,
fused image. The restoration of high frequency information lessens the degree of blurring in the fusedimage and hence improves its objective and subjective quality. Experimental result shows the proposed method achieves a Peak Signal to Noise Ratio (PSNR) improvement up to 0.9947dB than DCT interpolation and 2.8186dB than bicubic interpolation at 4:1 compression ratio.
This document provides an introduction to hidden Markov models (HMMs). It explains what HMMs are, where they are used, and why they are useful. Key aspects of HMMs covered include the Markov chain process, notation used in HMMs, an example of applying an HMM to temperature data, and the three main problems HMMs are used to solve: scoring observation sequences, finding optimal state sequences, and training a model. The document also outlines the forward, backward, and other algorithms used to efficiently solve these three problems.
An Algorithm for Bayesian Network Construction from Databutest
The document describes an algorithm for constructing Bayesian networks from data. The algorithm has three phases: drafting, thickening, and thinning. In the drafting phase, node pairs are ordered by mutual information and connected with arcs. Thickening adds arcs when nodes cannot be separated. Thinning examines arcs using conditional independence tests and removes arcs where nodes are independent. The algorithm was tested on an ALARM Bayesian network with 37 nodes and correctly learned the network structure from data in all three versions of the network.
Image Denoising Using Wavelet TransformIJERA Editor
In this project, we have studied the importance of wavelet theory in image denoising over other traditional methods. We studied the importance of thresholding in wavelet theory and the two basic thresholding method i.e. hard and soft thresholding experimentally. We also studied why soft thresholding is preferred over hard thresholding, three types of soft thresholding (Bayes shrink, Sure shrink, Visu shrink) as well as advantages and disadvantage of each of them
This paper proposes a new algorithm for single-image super-resolution that exploits image compressibility in the wavelet domain using compressed sensing theory. The algorithm incorporates the downsampling low-pass filter into the measurement matrix to decrease coherence between the wavelet basis and sampling basis, allowing use of wavelets. It then uses a greedy algorithm to solve for sparse wavelet coefficients representing the high-resolution image. Results show improved performance over existing super-resolution approaches without requiring training data.
A COMPARATIVE STUDY ON DISTANCE MEASURING APPROACHES FOR CLUSTERINGIJORCS
Clustering plays a vital role in the various areas of research like Data Mining, Image Retrieval, Bio-computing and many a lot. Distance measure plays an important role in clustering data points. Choosing the right distance measure for a given dataset is a biggest challenge. In this paper, we study various distance measures and their effect on different clustering. This paper surveys existing distance measures for clustering and present a comparison between them based on application domain, efficiency, benefits and drawbacks. This comparison helps the researchers to take quick decision about which distance measure to use for clustering. We conclude this work by identifying trends and challenges of research and development towards clustering.
Review of Use of Nonlocal Spectral – Spatial Structured Sparse Representation...IJERA Editor
This document summarizes a research paper that proposes a new method for hyperspectral image restoration using nonlocal spectral-spatial structured sparse representation. The key points are:
1) It introduces using nonlocal similarity and spectral-spatial structure of hyperspectral images in sparse representation models. Nonlocal similarity means similar image patches can be represented by shared dictionary atoms, distinguishing true signals from noise.
2) Using 3D blocks that exploit spectral and spatial correlations, rather than 2D patches, for sparse coding. This better distinguishes true signals and noise.
3) A mixed Poisson-Gaussian noise model is used to handle signal-dependent and signal-independent noise present in hyperspectral images. Variance-fitting transformation
Web image annotation by diffusion maps manifold learning algorithmijfcstjournal
Automatic image annotation is one of the most challenging problems in machine vision areas. The goal of this task is to predict number of keywords automatically for images captured in real data. Many methods are based on visual features in order to calculate similarities between image samples. But the computation cost of these approaches is very high. These methods require many training samples to be stored in memory. To lessen thisburden, a number of techniques have been developed to reduce the number
of features in a dataset. Manifold learning is a popular approach to nonlinear dimensionality reduction. In
this paper, we investigate Diffusion maps manifold learning method for webimage auto-annotation task.Diffusion maps
manifold learning method isused to reduce the dimension of some visual features. Extensive experiments and analysis onNUS-WIDE-LITE web image dataset with
different visual featuresshow how this manifold learning dimensionality reduction method can be applied effectively to image annotation.
Computer apparition plays the most important role in human perception, which is limited to only the visual band of the electromagnetic spectrum. The need for Radar imaging systems, to recover some sources that
are not within human visual band, is raised. This paper present new algorithm for Synthetic Aperture Radar (SAR) images segmentation based on thresholding technique. Entropy based image thresholding has
received sustainable interest in recent years. It is an important concept in the area of image processing.
Pal (1996) proposed a cross entropy thresholding method based on Gaussian distribution for bi-modal images. Our method is derived from Pal method that segment images using cross entropy thresholding based on Gamma distribution and can handle bi-modal and multimodal images. Our method is tested using
Synthetic Aperture Radar (SAR) images and it gave good results for bi-modal and multimodal images. The
results obtained are encouraging.
This document provides an overview of digital image processing. It discusses what image processing entails, including enhancing images, extracting information, and pattern recognition. It also describes various image processing techniques such as radiometric and geometric correction, image enhancement, classification, and accuracy assessment. Radiometric correction aims to reduce noise from sources like the atmosphere, sensors, and terrain. Geometric correction geometrically registers images. Image enhancement improves interpretability. Classification categorizes pixels. The document outlines both supervised and unsupervised classification methods.
This document presents research on content-based image retrieval using color and texture features. It proposes using both quadratic distance based on color histograms to measure color similarity, and pyramid structure wavelet transforms and gray level co-occurrence matrix (GLCM) to measure texture. For color features, quadratic distance is calculated between color histograms to retrieve similar images based on color. For texture, pyramid structure wavelet transforms are used to decompose images into sub-bands and calculate energy levels, while GLCM extracts texture statistics. The methods are evaluated on a dataset of 10000 images and results show the integrated approach of color and texture features provides more accurate and faster retrieval compared to individual features.
Hyperspectral image mixed noise reduction based on improved k svd algorithmeSAT Publishing House
This document summarizes a proposed algorithm for reducing mixed noise in hyperspectral imagery. Hyperspectral images capture information across the electromagnetic spectrum and can be represented as three-dimensional tensors. The proposed method uses tensor decomposition and an improved K-SVD algorithm to adaptively detect and remove Gaussian noise, impulse noise, and mixtures of these from hyperspectral data. It formulates the noise removal problem using a weighted regularization approach and solves related optimization problems using techniques like singular value decomposition. The goal is to separate noise and noise-free components to reconstruct a cleaned hyperspectral image tensor.
This summarizes a research paper that proposes a new approach for noise estimation on images. It uses wavelet transform because of its sparse nature, then applies a Bayesian approach by imposing a Gaussian distribution on transformed pixels. It checks image quality before noise estimation using maximum likelihood decision criteria. Then designs a new bound-based estimation process using ideas from Cramer-Rao lower bound for signals in additive white Gaussian noise. The experimental results show visually better output after reconstructing the original image.
Boosting ced using robust orientation estimationijma
In this paper, Coherence Enhancement Diffusion (CED) is boosted feeding external orientation using new
robust orientation estimation. In CED, proper scale selection is very important as the gradient vector at
that scale reflects the orientation of local ridge. For this purpose a new scheme is proposed in which pre
calculated orientation, by using local and integration scales. From the experiments it is found the proposed
scheme is working much better in noisy environment as compared to the traditional Coherence
Enhancement Diffusion
Comparative Study of Compressive Sensing Techniques For Image EnhancementCSCJournals
Compressive Sensing is a new way of sampling signals at a sub-Nyquist rate. For many signals, this revolutionary technology strongly relies on the sparsity of the signal and incoherency between sensing basis and representation basis. In this work, compressed sensing method is proposed to reduce the noise of the image signal. Noise reduction and image reconstruction are formulated in the theoretical framework of compressed sensing using Basis Pursuit de-noising (BPDN) and Compressive Sampling Matching Pursuit (CoSaMP) algorithm when random measurement matrix is utilized to acquire the data. Ultimately, it is demonstrated that the proposed methods can't perfectly recover the image signal. Therefore, we have used a complementary approach for enhancing the performance of CS recovery with non-sparse signals. In this work, we have used a new designed CS recovery framework, called De-noising-based Approximate Message Passing (D-AMP). This method uses a de-noising algorithm to recover signals from compressive measurements. For de-noising purpose the Non-Local Means (NLM), Bayesian Least Squares Gaussian Scale Mixtures (BLS-GSM) and Block Matching 3D collaborative have been used. Also, in this work, we have evaluated the performance of our proposed image enhancement methods using the quality measure peak signal-to-noise ratio (PSNR).
Wavelet-Based Warping Technique for Mobile Devicescsandit
The document proposes a wavelet-based warping technique to render novel views of compressed images on mobile devices. It uses Haar wavelet transform to compress large reference and depth images, reducing their size. The technique decomposes the images into approximation and detail parts, but only uses the approximation parts for warping. This improves rendering speed on mobile devices. The framework is implemented using Android tools and experiments show it provides faster rendering times for large images compared to direct warping without compression.
Image compression by ezw combining huffman and arithmetic encoderIAEME Publication
This document summarizes an article that proposes combining Embedded Zero tree Wavelet (EZW) image compression with Huffman and arithmetic encoders to achieve additional compression. EZW is an effective wavelet-based image compression algorithm that encodes coefficients in order of importance. The paper argues that applying Huffman coding followed by arithmetic encoding to the output of an EZW compressor provides around 15% extra compression with minimal quality loss. It describes the EZW encoding process, including the concept of zero trees that allows efficient coding of significance maps, and how discrete wavelet transforms decompose images into frequency subbands.
IMAGE SEGMENTATION BY USING THRESHOLDING TECHNIQUES FOR MEDICAL IMAGEScseij
Image binarization is the process of separation of pixel values into two groups, black as background and
white as foreground. Thresholding can be categorized into global thresholding and local thresholding. This
paper describes a locally adaptive thresholding technique that removes background by using local mean
and standard deviation. Most common and simplest approach to segment an image is using thresholding.
In this work we present an efficient implementation for threshoding and give a detailed comparison of
Niblack and sauvola local thresholding algorithm. Niblack and sauvola thresholding algorithm is
implemented on medical images. The quality of segmented image is measured by statistical parameters:
Jaccard Similarity Coefficient, Peak Signal to Noise Ratio (PSNR).
A Quantitative Comparative Study of Analytical and Iterative Reconstruction T...CSCJournals
A special image restoration problem is the reconstruction of image from projections – a problem of immense importance in medical imaging, computed tomography and non-destructive testing of objects. This is a problem where a two – dimensional (or higher) object is reconstructed from several one –dimensional projections [1]. The reconstruction techniques are broadly classified into three categories, analytical, iterative, and statistical [2]. The comparative study among these is of great importance in the field of medical imaging. This paper aims at comparative study by analyzing quantitatively the quality of image reconstructed by analytical and iterative techniques. Projections (parallel beam type) for the reconstruction are calculated analytically by defining Shepp logan phantom head model with coverage angle ranging from 0 to ±180o with rotational increment of 2o to 10o. For iterative reconstruction coverage angle of ±90o, iteration up to 10 is used. The original image is grayscale image of size 128 X 128. The Image quality of the reconstructed image is measured by six quality measurement parameters. In this paper as analytical technique; simple back projection and filtered back projection are implemented, while as iterative; algebraic reconstruction technique is implemented. Experiment result reveals that quality of reconstructed image increase as coverage angle, and number of views increases. The processing time is one major deciding component for reconstruction. Keywords: Reconstruction algorithm, Simple-Back projection algorithm (SBP), Filter-Back projection algorithm (FBP), Algebraic Reconstruction Technique algorithm (ART), Image quality, coverage angle, Computed tomography (CT).
Improved probabilistic distance based locality preserving projections method ...IJECEIAES
In this paper, a dimensionality reduction is achieved in large datasets using the proposed distance based Non-integer Matrix Factorization (NMF) technique, which is intended to solve the data dimensionality problem. Here, NMF and distance measurement aim to resolve the non-orthogonality problem due to increased dataset dimensionality. It initially partitions the datasets, organizes them into a defined geometric structure and it avoids capturing the dataset structure through a distance based similarity measurement. The proposed method is designed to fit the dynamic datasets and it includes the intrinsic structure using data geometry. Therefore, the complexity of data is further avoided using an Improved Distance based Locality Preserving Projection. The proposed method is evaluated against existing methods in terms of accuracy, average accuracy, mutual information and average mutual information.
Satellite image Compression reduces redundancy in data representation in order to achieve saving in the
cost of storage and transmission image compression compensates for the limited on-board resources, in
terms of mass memory and downlink bandwidth and thus it provides a solution to the (bandwidth vs. data
volume) dilemma of modern spacecraft Thus compression is very important feature in payload image
processing units of many satellites, In this paper, an improvement of the quantization step of the input
vectors has been proposed. The k-nearest neighbour (KNN) algorithm was used on each axis. The three
classifications considered as three independent sources of information, are combined in the framework of
the evidence theory the best code vector is then selected. After Huffman schemes is applied for encoding
and decoding.
An efficient fusion based up sampling technique for restoration of spatially ...ijitjournal
The various up-sampling techniques available in the literature produce blurring artifacts in the upsampled,
high resolution images. In order to overcome this problem effectively, an image fusion based interpolation technique is proposed here to restore the high frequency information. The Discrete Cosine Transform interpolation technique preserves low frequency information whereas Discrete Sine Transform preserves high frequency information. Therefore, by fusing the DCT and DST based up-sampled images, more high frequency, relevant information of both the up-sampled images can be preserved in the restored,
fused image. The restoration of high frequency information lessens the degree of blurring in the fusedimage and hence improves its objective and subjective quality. Experimental result shows the proposed method achieves a Peak Signal to Noise Ratio (PSNR) improvement up to 0.9947dB than DCT interpolation and 2.8186dB than bicubic interpolation at 4:1 compression ratio.
This document provides an introduction to hidden Markov models (HMMs). It explains what HMMs are, where they are used, and why they are useful. Key aspects of HMMs covered include the Markov chain process, notation used in HMMs, an example of applying an HMM to temperature data, and the three main problems HMMs are used to solve: scoring observation sequences, finding optimal state sequences, and training a model. The document also outlines the forward, backward, and other algorithms used to efficiently solve these three problems.
An Algorithm for Bayesian Network Construction from Databutest
The document describes an algorithm for constructing Bayesian networks from data. The algorithm has three phases: drafting, thickening, and thinning. In the drafting phase, node pairs are ordered by mutual information and connected with arcs. Thickening adds arcs when nodes cannot be separated. Thinning examines arcs using conditional independence tests and removes arcs where nodes are independent. The algorithm was tested on an ALARM Bayesian network with 37 nodes and correctly learned the network structure from data in all three versions of the network.
Image Denoising Using Wavelet TransformIJERA Editor
In this project, we have studied the importance of wavelet theory in image denoising over other traditional methods. We studied the importance of thresholding in wavelet theory and the two basic thresholding method i.e. hard and soft thresholding experimentally. We also studied why soft thresholding is preferred over hard thresholding, three types of soft thresholding (Bayes shrink, Sure shrink, Visu shrink) as well as advantages and disadvantage of each of them
Curved Wavelet Transform For Image Denoising using MATLAB.Nikhil Kumar
This document summarizes a student project on image denoising using wavelet analysis. It introduces wavelet transforms as a method to denoise digital images corrupted by noise. The project uses MATLAB to apply a discrete wavelet transform with a Haar wavelet, thresholds wavelet coefficients at different levels to compress and denoise the image, and demonstrates the results on an example image.
This document discusses using Bayesian networks for predictive analysis and machine learning perspectives on data utilization. It provides an example of using Bayesian networks to accurately predict incident clearance time based on variables like type of incident, number of police/ambulance vehicles, number of injuries, and number of vehicles involved. The document also discusses applying Bayesian networks by collecting current situation data as evidence to perform inference on a constructed inference model.
This document discusses image denoising techniques. It begins by defining image denoising as removing unwanted noise from an image to restore the original signal. It then discusses several types of noise like additive Gaussian noise, impulse noise, uniform noise, and periodic noise. For denoising, it covers spatial domain techniques like linear filters (mean, weighted mean), non-linear filters (median filter), and frequency domain techniques that apply a low-pass filter to the Fourier transform of the noisy image. The document provides examples of denoising noisy images using mean and median filters to remove different types of noise.
Bayesian Networks - A Brief IntroductionAdnan Masood
- A Bayesian network is a graphical model that depicts probabilistic relationships among variables. It represents a joint probability distribution over variables in a directed acyclic graph with conditional probability tables.
- A Bayesian network consists of a directed acyclic graph whose nodes represent variables and edges represent probabilistic dependencies, along with conditional probability distributions that quantify the relationships.
- Inference using a Bayesian network allows computing probabilities like P(X|evidence) by taking into account the graph structure and probability tables.
Hidden Markov Models with applications to speech recognitionbutest
This document provides an introduction to hidden Markov models (HMMs). It discusses how HMMs can be used to model sequential data where the underlying states are not directly observable. The key aspects of HMMs are: (1) the model has a set of hidden states that evolve over time according to transition probabilities, (2) observations are emitted based on the current hidden state, (3) the four basic problems of HMMs are evaluation, decoding, training, and model selection. Examples discussed include modeling coin tosses, balls in urns, and speech recognition. Learning algorithms for HMMs like Baum-Welch and Viterbi are also summarized.
Images may contain different types of noises. Removing noise from image is often the first step in image processing, and remains a challenging problem in spite of sophistication of recent research. This ppt presents an efficient image denoising scheme and their reconstruction based on Discrete Wavelet Transform (DWT) and Inverse Discrete Wavelet Transform (IDWT).
- Hidden Markov models (HMMs) are statistical models where the system is assumed to be a Markov process with hidden states. Each state has a number of possible transitions to other states, each with an assigned probability.
- There are three main issues in HMMs: model evaluation, decoding the most probable path, and model training.
- HMMs have applications in areas like speech recognition, gesture recognition, language modeling, and video analysis.
image denoising technique using disctere wavelet transformalishapb
This document discusses image denoising techniques using discrete wavelet transforms. It begins with an introduction and lists the objectives, goals, and types of noise that affect images. It then describes several denoising techniques including spatial filtering methods like mean, wiener and median filters as well as frequency domain filtering and wavelet domain filtering. The document provides block diagrams of the wavelet denoising process and evaluates performance of various denoising algorithms using metrics like PSNR and SSIM. It was implemented in MATLAB and concluded that wavelet thresholding provides significant improvement in image quality while preserving useful information.
Art is a creative expression that stimulates the senses or imagination according to Felicity Hampel. Picasso believed that every child is an artist but growing up can stop that creativity. Aristotle defined art as anything requiring a maker and not being able to create itself.
Review on Medical Image Fusion using Shearlet TransformIRJET Journal
This document reviews medical image fusion using the shearlet transform. It discusses how medical image fusion combines information from multimodality images like CT, MRI, PET into a single image. The shearlet transform allows for more efficient encoding of anisotropic features compared to wavelets. The proposed algorithm involves decomposing registered input images using shearlet transforms, applying fusion rules to select coefficients, and reconstructing the fused image. Medical image fusion using shearlets can improve diagnosis by combining complementary anatomical and functional details from different imaging modalities.
An Image representation using Compressive Sensing and Arithmetic Coding IJCERT
The demand for graphics and multimedia communication over intenet is growing day by day. Generally the coding efficiency achieved by CS measurements is below the widely used wavelet coding schemes (e.g., JPEG 2000). In the existing wavelet-based CS schemes, DWT is mainly applied for sparse representation and the correlation of DWT coefficients has not been fully exploited yet. To improve the coding efficiency, the statistics of DWT coefficients has been investigated. A novel CS-based image representation scheme has been proposed by considering the intra- and inter-similarity among DWT coefficients. Multi-scale DWT is first applied. The low- and high-frequency subbands of Multi-scale DWT are coded separately due to the fact that scaling coefficients capture most of the image energy. At the decoder side, two different recovery algorithms have been presented to exploit the correlation of scaling and wavelet coefficients well. In essence, the proposed CS-based coding method can be viewed as a hybrid compressed sensing schemes which gives better coding efficiency compared to other CS based coding methods.
The document proposes a hybrid method called Wavelet Embedded Anisotropic Diffusion (WEAD) for image denoising. WEAD is a two-stage filter that first applies anisotropic diffusion to reduce noise, followed by wavelet-based Bayesian shrinkage. This reduces the convergence time of anisotropic diffusion, allowing the image to be denoised with less blurring compared to anisotropic diffusion or wavelet methods alone. Experimental results on various images demonstrate that WEAD achieves better denoising performance than anisotropic diffusion or Bayesian shrinkage methods, as measured by higher PSNR and SSIM scores and fewer required iterations.
Fast Stereo Images Compression Method based on Wavelet Transform and Two dime...BRNSSPublicationHubI
This document proposes a fast stereo image compression method using discrete wavelet transform and two dimensional logarithmic (TDL) algorithm for motion estimation. It first applies discrete wavelet transform to the stereo images to reduce computation time. It then estimates the disparity between the images using TDL algorithm to find the motion vectors. It encodes the motion vectors with Huffman encoding while compressing the remaining image as a still image. Experimental results on test stereo image pairs show that the proposed method produces good results in terms of PSNR, compression ratio, and computation time compared to other motion estimation algorithms.
PCA & CS based fusion for Medical Image FusionIJMTST Journal
Compressive sampling (CS), also called Compressed sensing, has generated a tremendous amount of excitement in the image processing community. It provides an alternative to Shannon/ Nyquist sampling when the signal under acquisition is known to be sparse or compressible. In this paper, we propose a new efficient image fusion method for compressed sensing imaging. In this method, we calculate the two dimensional discrete cosine transform of multiple input images, these achieved measurements are multiplied with sampling filter, so compressed images are obtained. we take inverse discrete cosine transform of them. Finally, fused image achieves from these results by using PCA fusion method. This approach also is implemented for multi-focus and noisy images. Simulation results show that our method provides promising fusion performance in both visual comparison and comparison using objective measures. Moreover, because this method does not need to recovery process the computational time is decreased very much.
An efficient approach to wavelet image Denoisingijcsit
This document proposes an efficient approach to wavelet image denoising based on minimizing mean squared error. It uses Stein's unbiased risk estimate (SURE), which provides an accurate estimate of mean squared error without needing the original noiseless image. The key idea is to express the thresholding function as a linear combination of thresholds, allowing the minimization problem to be solved via a simple linear system rather than a nonlinear optimization. Experimental results show the proposed method achieves superior image quality compared to other techniques like BayesShrink and VisuShrink.
This document discusses performance of matching algorithms for signal approximation. It begins by introducing matching pursuit algorithms like Orthogonal Matching Pursuit (OMP) and Stagewise Orthogonal Matching Pursuit (StOMP) which are greedy algorithms that approximate sparse signals. It then describes the Non-Negative Least Squares algorithm which solves non-negative least squares problems. Finally, it discusses Extranious Equivalent Detection (EED), a modification of OED that incorporates non-negativity of representations by using a non-negative optimization technique instead of orthogonal projection.
Performance of Matching Algorithmsfor Signal Approximationiosrjce
The document summarizes and compares several algorithms for signal approximation and sparse signal recovery, including Equivalent Detection (ED), Non-negative Equivalent Detection, Orthogonal Matching Pursuit (OMP), and Stagewise Orthogonal Matching Pursuit (StOMP). It discusses how each algorithm works, including iteratively selecting atoms from a dictionary to build up a sparse representation of the signal. OMP selects one atom per iteration while StOMP selects all atoms above a threshold. The document also discusses computational complexities of the different algorithms.
Photoacoustic tomography based on the application of virtual detectorsIAEME Publication
This document discusses using virtual detectors to improve photoacoustic tomography (PAT) image reconstruction when full scanning data is unavailable. It proposes interpolation and compressed sensing methods to generate virtual detector data and increase the number of measurements. Simulation results show applying these methods to preprocessed photoacoustic data significantly improves the peak signal-to-noise ratio of reconstructed images compared to direct reconstruction with limited detectors. Dictionary-based compressed sensing provides the best performance by learning an over-complete dictionary to sparsify signals. The methods allow better quality PAT imaging when hardware and spatial constraints limit actual detector positions and sampling angles.
A common goal of the engineering field of signal processing is to reconstruct a signal from a series of sampling measurements. In general, this task is impossible because there is no way to reconstruct a signal during the times
that the signal is not measured. Nevertheless, with prior knowledge or assumptions about the signal, it turns out to
be possible to perfectly reconstruct a signal from a series of measurements. Over time, engineers have improved their understanding of which assumptions are practical and how they can be generalized. An early breakthrough in signal processing was the Nyquist–Shannon sampling theorem. It states that if the signal's highest frequency is less than half of the sampling rate, then the signal can be reconstructed perfectly. The main idea is that with prior knowledge about constraints on the signal’s frequencies, fewer samples are needed to reconstruct the signal. Sparse sampling (also known as, compressive sampling, or compressed sampling) is a signal processing technique for efficiently acquiring and reconstructing a signal, by finding solutions tounder determined linear systems. This is based on the principle that, through optimization, the sparsity of a signal can be exploited to recover it from far fewer samples than required by the Shannon-Nyquist sampling theorem. There are two conditions under which recovery is possible.[1] The first one is sparsity which requires the signal to be sparse in some domain. The second one is incoherence which is applied through the isometric property which is sufficient for sparse signals Possibility
of compressed data acquisition protocols which directly acquire just the important information Sparse sampling (CS) is a fast growing area of research. It neglects the extravagant acquisition process by measuring lesser values to reconstruct the image or signal. Sparse sampling is adopted successfully in various fields of image processing and proved its efficiency. Some of the image processing applications like face recognition, video encoding, Image encryption and reconstruction are presented here.
Comparative analysis of multimodal medical image fusion using pca and wavelet...IJLT EMAS
nowadays, there are a lot of medical images and their
numbers are increasing day by day. These medical images are
stored in large database. To minimize the redundancy and
optimize the storage capacity of images, medical image fusion is
used. The main aim of medical image fusion is to combine
complementary information from multiple imaging modalities
(Eg: CT, MRI, PET etc.) of the same scene. After performing
image fusion, the resultant image is more informative and
suitable for patient diagnosis. There are some fusion techniques
which are described in this paper to obtain fused image. This
paper presents two approaches to image fusion, namely Spatial
Fusion and Transform Fusion. This paper describes Techniques
such as Principal Component Analysis which is spatial domain
technique and Discrete Wavelet Transform, Stationary Wavelet
Transform which are Transform domain techniques.
Performance metrics are implemented to evaluate the
performance of image fusion algorithm. An experimental result
shows that image fusion method based on Stationary Wavelet
Transform is better than Principal Component Analysis and
Discrete Wavelet Transform.
A MODIFIED HISTOGRAM BASED FAST ENHANCEMENT ALGORITHMcscpconf
The contrast enhancement of medical images has an important role in diseases diagnostic,
specially, cancer cases. Histogram equalization is considered as the most popular algorithm for
contrast enhancement according to its effectiveness and simplicity. In this paper, we present a
modified version of the Histogram Based Fast Enhancement Algorithm. This algorithm
enhances the areas of interest with less complexity. It is applied only to CT head images and its
idea based on treating with the soft tissues and ignoring other details in the image. The
proposed modification make the algorithm is valid for most CT image types with enhanced
results.
EXTENDED WAVELET TRANSFORM BASED IMAGE INPAINTING ALGORITHM FOR NATURAL SCENE...cscpconf
This paper proposes an exemplar based image inpainting using extended wavelet transform. The
Image inpainting modifies an image with the available information outside the region to be
inpainted in an undetectable way. The extended wavelet transform is in two dimensions. The
Laplacian pyramid is first used to capture the point discontinuities, and then followed by a
directional filter bank to link point discontinuities into linear structures. The proposed model
effectively captures the edges and contours of natural scene images
This document discusses and compares different thresholding techniques for image denoising using wavelet transforms. It introduces the concept of image denoising using wavelet transforms, which involves applying a forward wavelet transform, estimating clean coefficients using thresholding, and applying the inverse transform. It then describes several common thresholding methods - hard, soft, universal, improved, Bayes shrink, and neigh shrink. Simulation results on test images corrupted with additive white Gaussian noise show that the proposed improved thresholding technique achieves lower MSE and higher PSNR than the universal hard thresholding method, demonstrating better noise removal performance while preserving image details.
This document discusses different techniques for image denoising using wavelet thresholding. It begins with an introduction to image denoising and the wavelet transform approach. Then it describes various thresholding methods used in wavelet-based image denoising, including hard, soft, universal, improved, Bayes shrink, and neigh shrink thresholding. It also reviews prior literature comparing these different techniques. Finally, it presents simulated results on test images comparing the performance of universal hard thresholding and improved thresholding based on mean squared error and peak signal-to-noise ratio metrics under varying levels of additive white Gaussian noise. The improved thresholding method achieved better denoising performance according to the quantitative metrics.
This paper presents an approach for image restoration in the presence of blur and noise. The image is divided into independent regions modeled with a Gaussian prior. Wavelet-based methods are used for image denoising, while classical Wiener filtering is used for deblurring. The algorithm finds the maximum a posteriori estimate at the intersection of convex sets generated by Wiener filtering. It provides efficient image restoration without sacrificing the simplicity of filtering, and generates a better restored image compared to previous methods.
This paper presents an approach for image restoration in the presence of blur and noise. The image is divided into independent regions modeled with a Gaussian prior. Wavelet based methods are used for image denoising, while classical Wiener filtering is used for deblurring. The algorithm finds the maximum a posteriori estimate at the intersection of convex sets generated by Wiener filtering. It provides efficient image restoration without sacrificing the simplicity of filtering, and generates a better restored image.
A MODIFIED HISTOGRAM BASED FAST ENHANCEMENT ALGORITHMcsandit
The contrast enhancement of medical images has an important role in diseases diagnostic,
specially, cancer cases. Histogram equalization is considered as the most popular algorithm for
contrast enhancement according to its effectiveness and simplicity. In this paper, we present a
modified version of the Histogram Based Fast Enhancement Algorithm. This algorithm
enhances the areas of interest with less complexity. It is applied only to CT head images and its
idea based on treating with the soft tissues and ignoring other details in the image. The
proposed modification make the algorithm is valid for most CT image types with enhanced
results.
A MODIFIED HISTOGRAM BASED FAST ENHANCEMENT ALGORITHMcsandit
This document proposes a modified version of the Histogram Based Fast Enhancement Algorithm to improve contrast enhancement of medical images like CT scans. The key modifications are:
1) Calculating the value of k, which determines how many gray levels are ignored, as a ratio of the mean, median, or mode of the histogram rather than a constant value. This makes k adaptive to each image.
2) Applying the modified algorithm to a wide range of CT image types, not just head images, to validate it for more cases.
3) Evaluating the modified algorithm using metrics like PSNR, AMBE, and entropy, as well as visual inspection. Results show the modified algorithm achieves better contrast enhancement
Application of Bayes Compressed Sensing in Image rocessingIJRESJOURNAL
This document discusses applying Bayes compressed sensing to image processing. It proposes a nonparametric hierarchical Bayes model using a Dirichlet process distribution for sparse representation of image compression. The model can learn a low-dimensional Gaussian mixture model to represent high-dimensional image data restricted to low-dimensional subspaces, obtaining the number of mixed factors through automatic learning. Simulation experiments show the effectiveness of using the model as prior knowledge for image compressed sensing reconstruction.
Similar to Clustered Compressive Sensingbased Image Denoising Using Bayesian Framework (20)
GraphRAG for Life Science to increase LLM accuracyTomaz Bratanic
GraphRAG for life science domain, where you retriever information from biomedical knowledge graphs using LLMs to increase the accuracy and performance of generated answers
Ocean lotus Threat actors project by John Sitima 2024 (1).pptxSitimaJohn
Ocean Lotus cyber threat actors represent a sophisticated, persistent, and politically motivated group that poses a significant risk to organizations and individuals in the Southeast Asian region. Their continuous evolution and adaptability underscore the need for robust cybersecurity measures and international cooperation to identify and mitigate the threats posed by such advanced persistent threat groups.
HCL Notes and Domino License Cost Reduction in the World of DLAUpanagenda
Webinar Recording: https://www.panagenda.com/webinars/hcl-notes-and-domino-license-cost-reduction-in-the-world-of-dlau/
The introduction of DLAU and the CCB & CCX licensing model caused quite a stir in the HCL community. As a Notes and Domino customer, you may have faced challenges with unexpected user counts and license costs. You probably have questions on how this new licensing approach works and how to benefit from it. Most importantly, you likely have budget constraints and want to save money where possible. Don’t worry, we can help with all of this!
We’ll show you how to fix common misconfigurations that cause higher-than-expected user counts, and how to identify accounts which you can deactivate to save money. There are also frequent patterns that can cause unnecessary cost, like using a person document instead of a mail-in for shared mailboxes. We’ll provide examples and solutions for those as well. And naturally we’ll explain the new licensing model.
Join HCL Ambassador Marc Thomas in this webinar with a special guest appearance from Franz Walder. It will give you the tools and know-how to stay on top of what is going on with Domino licensing. You will be able lower your cost through an optimized configuration and keep it low going forward.
These topics will be covered
- Reducing license cost by finding and fixing misconfigurations and superfluous accounts
- How do CCB and CCX licenses really work?
- Understanding the DLAU tool and how to best utilize it
- Tips for common problem areas, like team mailboxes, functional/test users, etc
- Practical examples and best practices to implement right away
Let's Integrate MuleSoft RPA, COMPOSER, APM with AWS IDP along with Slackshyamraj55
Discover the seamless integration of RPA (Robotic Process Automation), COMPOSER, and APM with AWS IDP enhanced with Slack notifications. Explore how these technologies converge to streamline workflows, optimize performance, and ensure secure access, all while leveraging the power of AWS IDP and real-time communication via Slack notifications.
Essentials of Automations: The Art of Triggers and Actions in FMESafe Software
In this second installment of our Essentials of Automations webinar series, we’ll explore the landscape of triggers and actions, guiding you through the nuances of authoring and adapting workspaces for seamless automations. Gain an understanding of the full spectrum of triggers and actions available in FME, empowering you to enhance your workspaces for efficient automation.
We’ll kick things off by showcasing the most commonly used event-based triggers, introducing you to various automation workflows like manual triggers, schedules, directory watchers, and more. Plus, see how these elements play out in real scenarios.
Whether you’re tweaking your current setup or building from the ground up, this session will arm you with the tools and insights needed to transform your FME usage into a powerhouse of productivity. Join us to discover effective strategies that simplify complex processes, enhancing your productivity and transforming your data management practices with FME. Let’s turn complexity into clarity and make your workspaces work wonders!
In his public lecture, Christian Timmerer provides insights into the fascinating history of video streaming, starting from its humble beginnings before YouTube to the groundbreaking technologies that now dominate platforms like Netflix and ORF ON. Timmerer also presents provocative contributions of his own that have significantly influenced the industry. He concludes by looking at future challenges and invites the audience to join in a discussion.
Your One-Stop Shop for Python Success: Top 10 US Python Development Providersakankshawande
Simplify your search for a reliable Python development partner! This list presents the top 10 trusted US providers offering comprehensive Python development services, ensuring your project's success from conception to completion.
Have you ever been confused by the myriad of choices offered by AWS for hosting a website or an API?
Lambda, Elastic Beanstalk, Lightsail, Amplify, S3 (and more!) can each host websites + APIs. But which one should we choose?
Which one is cheapest? Which one is fastest? Which one will scale to meet our needs?
Join me in this session as we dive into each AWS hosting service to determine which one is best for your scenario and explain why!
Full-RAG: A modern architecture for hyper-personalizationZilliz
Mike Del Balso, CEO & Co-Founder at Tecton, presents "Full RAG," a novel approach to AI recommendation systems, aiming to push beyond the limitations of traditional models through a deep integration of contextual insights and real-time data, leveraging the Retrieval-Augmented Generation architecture. This talk will outline Full RAG's potential to significantly enhance personalization, address engineering challenges such as data management and model training, and introduce data enrichment with reranking as a key solution. Attendees will gain crucial insights into the importance of hyperpersonalization in AI, the capabilities of Full RAG for advanced personalization, and strategies for managing complex data integrations for deploying cutting-edge AI solutions.
Best 20 SEO Techniques To Improve Website Visibility In SERPPixlogix Infotech
Boost your website's visibility with proven SEO techniques! Our latest blog dives into essential strategies to enhance your online presence, increase traffic, and rank higher on search engines. From keyword optimization to quality content creation, learn how to make your site stand out in the crowded digital landscape. Discover actionable tips and expert insights to elevate your SEO game.
OpenID AuthZEN Interop Read Out - AuthorizationDavid Brossard
During Identiverse 2024 and EIC 2024, members of the OpenID AuthZEN WG got together and demoed their authorization endpoints conforming to the AuthZEN API
In the rapidly evolving landscape of technologies, XML continues to play a vital role in structuring, storing, and transporting data across diverse systems. The recent advancements in artificial intelligence (AI) present new methodologies for enhancing XML development workflows, introducing efficiency, automation, and intelligent capabilities. This presentation will outline the scope and perspective of utilizing AI in XML development. The potential benefits and the possible pitfalls will be highlighted, providing a balanced view of the subject.
We will explore the capabilities of AI in understanding XML markup languages and autonomously creating structured XML content. Additionally, we will examine the capacity of AI to enrich plain text with appropriate XML markup. Practical examples and methodological guidelines will be provided to elucidate how AI can be effectively prompted to interpret and generate accurate XML markup.
Further emphasis will be placed on the role of AI in developing XSLT, or schemas such as XSD and Schematron. We will address the techniques and strategies adopted to create prompts for generating code, explaining code, or refactoring the code, and the results achieved.
The discussion will extend to how AI can be used to transform XML content. In particular, the focus will be on the use of AI XPath extension functions in XSLT, Schematron, Schematron Quick Fixes, or for XML content refactoring.
The presentation aims to deliver a comprehensive overview of AI usage in XML development, providing attendees with the necessary knowledge to make informed decisions. Whether you’re at the early stages of adopting AI or considering integrating it in advanced XML development, this presentation will cover all levels of expertise.
By highlighting the potential advantages and challenges of integrating AI with XML development tools and languages, the presentation seeks to inspire thoughtful conversation around the future of XML development. We’ll not only delve into the technical aspects of AI-powered XML development but also discuss practical implications and possible future directions.
For the full video of this presentation, please visit: https://www.edge-ai-vision.com/2024/06/building-and-scaling-ai-applications-with-the-nx-ai-manager-a-presentation-from-network-optix/
Robin van Emden, Senior Director of Data Science at Network Optix, presents the “Building and Scaling AI Applications with the Nx AI Manager,” tutorial at the May 2024 Embedded Vision Summit.
In this presentation, van Emden covers the basics of scaling edge AI solutions using the Nx tool kit. He emphasizes the process of developing AI models and deploying them globally. He also showcases the conversion of AI models and the creation of effective edge AI pipelines, with a focus on pre-processing, model conversion, selecting the appropriate inference engine for the target hardware and post-processing.
van Emden shows how Nx can simplify the developer’s life and facilitate a rapid transition from concept to production-ready applications.He provides valuable insights into developing scalable and efficient edge AI solutions, with a strong focus on practical implementation.
Cosa hanno in comune un mattoncino Lego e la backdoor XZ?Speck&Tech
ABSTRACT: A prima vista, un mattoncino Lego e la backdoor XZ potrebbero avere in comune il fatto di essere entrambi blocchi di costruzione, o dipendenze di progetti creativi e software. La realtà è che un mattoncino Lego e il caso della backdoor XZ hanno molto di più di tutto ciò in comune.
Partecipate alla presentazione per immergervi in una storia di interoperabilità, standard e formati aperti, per poi discutere del ruolo importante che i contributori hanno in una comunità open source sostenibile.
BIO: Sostenitrice del software libero e dei formati standard e aperti. È stata un membro attivo dei progetti Fedora e openSUSE e ha co-fondato l'Associazione LibreItalia dove è stata coinvolta in diversi eventi, migrazioni e formazione relativi a LibreOffice. In precedenza ha lavorato a migrazioni e corsi di formazione su LibreOffice per diverse amministrazioni pubbliche e privati. Da gennaio 2020 lavora in SUSE come Software Release Engineer per Uyuni e SUSE Manager e quando non segue la sua passione per i computer e per Geeko coltiva la sua curiosità per l'astronomia (da cui deriva il suo nickname deneb_alpha).
2. 186 Computer Science & Information Technology (CS & IT)
image data to frequency or time-frequency domain, respectively. The later transform method have
been used intensively due to the fact that the Wavelet transform based methods surpasses the
others in the sense of mean square error (MSE) or pick signal to noise ratio (PSNR) and other
performance metrics [1], [2], [3].
Recently, another way of image denoising has been used after a new way of signal processing
method called compressive sensing (CS) was revived by authors like Donoho, Candés, Romberg
and Tao [4]- [7]. CS is a method to capture information at lower rate than the Nyquist- Shannon
sampling rate when signals are sparse or sparse in some domain. It has already been applied in
medical imaging. In [8] the authors have used the sparsity of magnetic resonance imaging (MRI)
signals and showed that this can be exploited to significantly reduce scan time, or alternatively,
improve the resolution of MR imagery and in [9] it is applied for Biological Microscopy image
denoising to reduce exposure time along with photo- toxicity and photo-bleaching. Since CS-
based denoising is done using reduced amount of data or measurement. Actually, it can remove
noise better than the state-of the art methods while using few measurements and preserving the
perceptual quality [10]. This paper builds up on the CS based denoising and incorporates it with
the clustredness of some image data. This is done using a statistical method called Bayesian
framework.
There are two schools of thoughts called the classical (also called the frequentist) and the
Bayesian in the statistical world. Their basic difference arises from the basic definition of
probability. Frequentists define P(x) as a long-run relative frequency with which x occurs in
identical repeats of an experiment. Where as Bayesian defines P(x|y) as a real number measure of
the probability of a proposition x, given the truth of the information represented by proposition y.
So under Bayesian theory, probability is considered as an extension of logic. Probabilities
represent the investigators degree of belief- hence it is subjective. That belief or prior information
is an integral part of the inference done by the Bayesian [11] - [20]. For its flexibility and
robustness this paper focuses on Bayesian approach. Specifically the prior information’s like
sparsity and clusterdness (or structures on the patterns of sparsity) of an image as two different
priors are used and the noise is removed by using reconstructing algorithms.
Our contribution in this work is to use the Bayesian framework and incorporate two different
priors in order to remove the noise in an image data and in addition we compare different
algorithms. Therefore, this paper is organized as follows. In section II we discuss the problem of
denosing using the CS theory under the Bayesian framework, that is using two priors on the data,
the sparse and clustered priors, and define the denosing problem in this context. In section III we
provide how we implemented the analysis. Section IV shows our results using synthetic and MRI
data, and section V presents conclusion and future work.
2. COMPRESSED SENSING BASED DENOISING
In Wavelet based transform denosing the image data is transformed to time-frequency domain
using Wavelet. Only the largest coefficients are kept and the rest are thrown away using
thresholding. Then by applying the inverse Wavelet transform the image is denoised [21],
however, in this paper we used CS recovery as denosing.
Considering an image which is sparse or sparse in some domain, which has sparse representation
in some domain or most of the energy of the image is compressed in few coefficients, say ݔ ϵ ℝ
with non zero elements k, corrupted by noise n ϵ ℝ
. It is possible to use different models of
noise distribution. By using a measurement matrix A ϵ ℝ×
, we get a noisy and under sampled
measurements ݕ ϵ ℝ
. Further we assume that w = An ϵ ℝ
is i.i.d. Gaussian random variables
with zero mean and covariance matrix σଶ
I, due to the central limit theorem. This assumption can
3. Computer Science & Information Technology (CS & IT) 187
be improved further. However, in this work we approximate it by Gaussian distribution for .ݓ
The linear model that relates these variables is given by
ݕ = ݔܣ ݓ 2.1
Here ܰ ≫ ܯ and ܰ ≫ ݇, where ݇ is the number of nonzero entries in .ݔ Applying CS
reconstructions using different algorithms we recover the estimate of the original signal ,ݔ say ݔො.
In this paper, denosing is done simultaneously with reconstructing the true image data using non-
linear reconstruction schemes, which are robust, [22] and the block diagram describing the whole
process is given by Figure 1.
Figure 1: Block diagram for CS based denosing.
Various methods for reconstructing ݔ may be used. We have the least square (LS) estimator in
which no prior information is applied:
ݔො = ሺܣ்
ܣሻିଵ
ܣ்
,ݕ 2.2
which performs very badly for the CS based denoising problem considered here. Another
approach to reconstruct ݔ is via the solution of the unconstrained optimization problem
ݔො = min୶ ℝొ
ଵ
ଶ
‖ݕ െ ‖ݔܣଶ
ଶ
݂ݑሺݔሻ 2.3
where ݂ݑሺݔሻ is a regularizing term, for some non-negative .ݑ If ݂ሺݔሻ = ‖ݔ ‖, emphasis is
made on a solution which shall LP norm, and = norm, and ‖ݔ ‖ is denoted a penalizing norm.
When = 2, we get
ݔො = min୶ ℝొ
ଵ
ଶ
‖ݕ െ ‖ݔܣଶ
ଶ
ݔ‖ݑ ‖ଶ. 2.4
This is penalizing the least square error by the L2 norm and this performs bad as well, since it
does not introduce sparsity into the problem. When = 0, we get the L0 norm, which is defined
as
‖ݔ ‖ = ݇ ≡ ሼ݅ ߳ ሼ1,2, … , ܰሽ|ݔ ് 0ሽ,
the number of the non zero entries of ,ݔ which actually is a partial norm since it does not satisfy
the triangle inequality property, but can be treated as norm by defining it as in [23], and get the
L0 norm regularizing estimator
ݔො = min୶ ℝొ
ଵ
ଶ
‖ݕ െ ‖ݔܣଶ
ଶ
ݔ‖ݑ ‖ 2.5
which gives the best solution for the problem at hand since it favour’s sparsity in .ݔ Nonetheless,
it is an NP- hard combinatorial problem. Instead, it has been a practice that one reconstructs the
image using L1 penalizing norm to get the estimator
4. 188 Computer Science & Information Technology (CS & IT)
ݔො = min୶ ℝొ
ଵ
ଶ
‖ݕ െ ‖ݔܣଶ
ଶ
ݔ‖ݑ ‖ଵ 2.6
which is a convex approximation to the L0 penalizing solution II.5. These estimators, 2.4 - 2.6,
can equivalently be presented as solutions to constrained optimization problem [4] - [7], and in
the CS literature there are many different types of algorithms to implement them. A very popular
one is the L1 penalized L2 minimization called LASSO (Least Absolute Shrinkage and Selection
Operator), which we later will present it in Bayesian framework. So first we present what a
Bayesian approach is and come back to the problem at hand.
2.1. Bayesian framework
Under Bayesian inference consider two random variables ݔ and ݕ with probability density
function (pdf) ሺݔሻ and ሺݕሻ, respectively. Using Bayes’ theorem it is possible to show that the
posterior distribution, ሺݕ|ݔሻ, is proportional to the product of the likelihood function, ሺݔ|ݕሻ,
and the prior distribution, ሺݔሻ,
ሺݕ|ݔሻ ∝ ሺݔ|ݕሻሺݔሻ 2.7
Equation (2.7) is called Updating Rule in which the data allows us to update our prior views
about .ݔ And as a result we get the posterior which combines both the data and non-data
information of ݔ [11], [12], [20].
Further, the Maximum a posterior (MAP), ݔොெ, is given by
ݔොெ = arg max௫ ሺݔ|ݕሻሺݔሻ
To proceed further, we assume two prior distributions on .ݔ
2.2. Sparse Prior
The reconstruction of ݔ resulting from the estimator (2.3) for the sparse problem we consider in
this paper given by, (2.4) - (2.5), can be presented as a maximum a posteriori (MAP) estimator
under the Bayesian framework as in [23]. We show this by defining a prior probability
distribution for ݔ on the form
ሺݔሻ =
షೠሺೣሻ
షೠሺೣሻௗ௫ೣ ച ℝಿ
2.8
where the regulirizing function ݂ ∶ ߯ → ܴ is some scalarvalued, non negative function with
߯ ⊆ ℝ which can be expanded to a vector argument by
݂ሺݔሻ = ∑ ݂ሺݔሻே
ୀଵ 2.9
such that for sufficiently large ,ݑ ݁ି௨ሺ௫ሻ
݀ݔ௫ ఢ ℝಿ is finite. Further, let the assumed variance of
the noise be given by
ߪଶ
=
ߣ
ݑ
where ߣ is system parameter which can be taken as ߣ = ߪଶ
.ݑ Note that the prior, (2.8), is
defined in such a way that it can incorporate the different estimators considered above by
5. Computer Science & Information Technology (CS & IT) 189
assuming different penalizing terms via ݂ሺݔሻ [23]. Further, the liklihood function, ሺݔ|ݕሻ, can be
shown to be
p୷|୶ሺy|xሻ =
ଵ
ሺଶሻొ/మ e
ି
భ
మಚమ‖୷ି୶‖మ
మ
2.10
the posterior, pሺx|yሻ,
p୶|୷ሺx|y; Aሻ =
e
ି
ଵ
ଶమ‖୷ି୶‖మ
మ
ሺ2πσሻ/ଶ ୣ
ష౫ሺ
భ
మಓ
‖౯షఽ౮‖మ
మశಓሺ౮ሻሻ
ୢ୶౮ ಣ ℝొ
and the MAP estimator becomes
xො = arg min୶ ℝొ
ଵ
ଶ
‖y െ Ax‖ଶ
ଶ
λfሺxሻ 2.11
as shown in [20]. Note that (2.11) which is equivalent to (2.3). Now, as we choose different
regularizing function, which enforces sparsity into the vector x, we get different estimators listed
below [23]:
1) Linear Estimators: when fሺxሻ = ‖x‖ଶ
ଶ
(2.11) reduces to
xො୧୬ୣୟ୰ = A
൫AA
λI൯
ିଵ
y, 2.12
which is the LMMSE estimator. But we ignore this estimator in our analysis since the
following two estimators are more interesting for CS problems.
2) LASSO Estimator: when fሺxሻ = ‖x‖ଵ we get the LASSO estimator and (II.11) becomes,
xොୗୗ = arg min୶ ℝొ
ଵ
ଶ
‖y െ Ax‖ଶ
ଶ
λ‖x‖ଵ, 2.13
which is the same as (2.6).
3) Zero-Norm regularization estimator: when ݂ሺxሻ = ‖x‖, we get the Zero-Norm
regularization estimator (2.5) to reconstruct the image from the noisy data and (2.11)
becomes
xොୣ୰୭ି୭୰୫ = arg min୶ ℝొ
ଵ
ଶ
‖y െ Ax‖ଶ
ଶ
λ‖x‖, 2.14
which is identical to 2.5. As mentioned earlier, this is the best solution for reconstruction of the
sparse vector ,ݔ but is NP-complete. The worst reconstruction for the sparse problem considered
is the L2- regularization solution given by (2.12). However, the best one is given by the equation
(2.13) and its equivalent forms such as L1-norm regularized least-squares (L1-LS) and others [5]-
[7].
2.3. Clustering Prior
Building on the Bayesian philosophy, we can further assume another prior distributions for
clustering. The entries of the sparse vector ݔ may have some structure that can be represented
using distributions. In [18] a hierarchical Bayesian generative model for sparse signals is found in
6. 190 Computer Science & Information Technology (CS & IT)
which they have applied full Bayesian analysis by assuming prior distributions to each parameter
appearing in the analysis. We follow a different approach. Instead we use another penalizing
parameter to represent clusterdness in the data. For that we define the clustering using the
distance between the entries of the sparse vector ݔ by
ܦሺݔሻ ≡ ∑ |ݔ െ ݔିଵ|ே
ୀଶ ,
and we use a regularizing parameter . Hence, we define the clustering prior to be
ݍሺݔሻ =
షംವሺೣሻ
షംವሺೣሻௗ௫౮ ಣ ℝొ
2.15
The new posterior involving this prior under the Bayesian framework is proportional to the
product of the three pdf’s:
pሺx|y) ∝ p(y|x)p(x)q(x). 2.16
By similar arguments as used in 2.2 we arrive at the Clustered LASSO estimator
xොେ୪୳ିୗୗ = arg min୶ ℝొ
ଵ
ଶ
‖y − Ax‖ଶ
ଶ
+ λ‖x‖ଵ + ߛ ∑ |ݔ − ݔିଵ|ே
ୀଶ , 2.17
where λ, γ are our tuning parameters for the sparsity in ݔ and the way the entries are clustered,
respectively.
3. IMPLEMENTATION OF THE ANALYSIS
The main focus of this paper is to give a practical application of compressed sensing, namely
denoising. That is we interpret the reconstruction of images by CS algorithms, given relatively
few measurements y and measurement matrix A, as denosing. That means the CS based denosing
happens when we apply the reconstructing schemes. Actually, we have used both CS based
(LMMSE, LASSO and Clustered LASSO given by equations (2.12), (2.13), (2.17) respectively)
and non-CS based denoising procedures (LS (2.2); BM3D). So that we compare the merits and
draw backs of CS based denoising techniques.
In the equations (2.12) , (2.13), and (2.17) we have parameters like λ and γ. As we have based our
analysis in Bayesian framework we could have assumed some prior distributions on each of them,
and build a hierarchical Bayesian compressive sensing. Instead we have used them as a tuning
parameter for the constraint and we have tried to use them in the optimal way. Still it needs more
work! However, we have found an optimal λ value for the LMMSE in (2.12), that is λ = 1e−07. In
implementing (2.13), that is least square optimization with L1 regularization, we have used the
Quadratic programming with constraints similar to Tibshirani [24], [25]. That is solving
xො = arg min୶ ‖y − Ax‖ଶ
ଶ
3.1
ݐ݆ܾܿ݁ݑݏ ݐ ‖x‖ଵ ≤ t,
instead of (2.13). We see that ݐ and λ are related.
In addition, equation (II.17) is implemented similar to LASSO with additional term on the
constraint. That is we bounded )ݔ(ܦ ≤ ݀. This ݀ is some how related to γ, i.e., we put constrain
on the neighboring elements. Since we have vectorized the image for the sake of efficiency of the
algorithm, the penalizing terms are applied column wise. Other ways of implementing
7. Computer Science & Information Technology (CS & IT) 191
(constraining) are also possible. But we differ it for future work. In our simulations we have used
optimal values of these constraints. Figure 2 and 3 show the respective optimal values for one of
the simulations in the next section.
Figure 1: This figure shows the MSE of LASSO and clustered LASSO for different values of ݐ for figure
4. It can be seen that there is only one optimal value.
Figure 2: This figure shows the MSE of LASSO and clustered LASSO for different values of ࢊ for figure
4. It can be seen that there is only one optimal value d and by loosening the constraint clustered LASSO
will converge to LASSO.
4. RESULTS
4.1 First set of Synthetic Data
In order to demonstrate the performance of reconstruction of the sparse signal (denosing)
presented in the paper we have used synthetic data. The first set of data is the image with several
English letters, where the image itself is sparse and clustered in the spatial domain. We have
applied Gaussian noise with mean zero and variance σ2 = 0.2 and random matrix ܣ with Gaussian
entries with variance σ2 = 1. For LMMSE we used λ = 1e − 07 in our simulations. However, we
have used equivalent constraints for λ and γ for the LASSO and clustered LASSO.
8. 192 Computer Science & Information Technology (CS & IT)
The original signal after vectorization is ݔ is of length N = 300 and we added noise to it. By
taking 244 measurements, that is y is of length M = 244, and maximum number of non-zero
elements k = 122, we applied different denosing techniques. There are several CS reconstructing
algorithms like LMMSE, LASSO and Clustered LASSO, which are used as denosing techniques
in this paper. In addition, the state of the art denosing technique, called Block-matching and 3D
filtering (BM3D) (http://www.cs.tut.fi/foi/GCF-BM3D/) [26], is used as reference. Note that
BM3D uses full measurements in contrast to the CS based denoising methods. The results are
shown in figure 4. The result in figure 4 shows that denosing using clustered LASSO performs
better than other methods, which use fewer measurements. However, BM3D, which uses full
measurements, has better performance. This is also visible in Table I, by using the performance
metrics like the mean square error (MSE) and pick signal to noise ratio (PSNR). However, it is
possible to improve the performance of clustered LASSO by considering other forms of
clustering, which will be our future work.
TABLE I: Performance comparison in figure 4
Algorithm MSE PSNR in dB
LS 0.41445 7.6506
LMMSE 0.14623 16.699
LASSO 0.11356 18.8955
Clustered LASSO 0.082645 27.1302
BM3D 0.044004 21.6557
Figure 3: Comparison of denosing techniques for the synthetic image: a) Original image x b) Noisy image
c) Least Square (LS) d) LMMSE e ) LASSO f) Clustered Lasso g) BM3D.
4.2 Second set of Synthetic Data
On this image we added different noise models such as Gaussian with mean 0 and variance 0.01,
Salt & pepper with noise density 0.03, and Speckle noise, i.e. with uniform distribution zero mean
and variance 0.3. Clustered LASSO performs consistently better than LASSO. The original signal
after vectorization is ݔ is of length N = 300 and we added noise to it. By taking 185
measurements, that is ݕ is of length M = 185, and maximum number of non-zero elements k = 84,
we applied different denosing techniques. The results in figure 5 are interesting. Because
clustered LASSO has higher PSNR than BM3D as shown in Table II.
9. Computer Science & Information Technology (CS & IT) 193
TABLE II: Performance comparison in figure 5
Algorithm Gaussian (0, 0.01) Salt & pepper Speckle
LS 2.3902 4.3149 8.9765
LMMSE 26.4611 24.6371 24.8943
LASSO 17.9837 22.6761 30.8123
Clustered LASSO 32.1578 40.6193 37.3392
BM3D 41.6925 32.1578 32.7813
Figure 4: Application of different denosing techniques discussed in the paper (in their vertical order: LS,
LMMSE, LASSO, Clustered LASSO, BM3D) on different types of noises (in the vertical order: Gaussian
with mean 0 & variance 0.01, Slat & Pepper with 0.03 and Speckle 0.3) .
4.3 Phantom image
The third image is a known medical related image, Shepp-Logan phantom, which is not sparse in
spatial domain but in K-space. We add noise to it, and we took the noisy image to K-space. After
that we zero out small coefficients and apply the CS denoising methods and then converted it
back to spatial domain. But for BM3D we used only the noisy image in the spatial domain. The
original signal after vectorization is ݔ is of length N = 200. By taking 138 measurements, that is y
is of length M = 138, and maximum number of non-zero elements k = 69, we applied different
denosing techniques. The result shows clustered LASSO does well compared to the others CS
algorithms and LS. But it is inferior to BM3D, which uses full measurement. This can be seen in
figure 6 and Table III.
10. 194 Computer Science & Information Technology (CS & IT)
TABLE I: Performance comparison in figure 6
Algorithm MSE PSNR in dB
LMMSE 0.016971 35.4057
LASSO 0.0061034 44.2885
Clustered LASSO 0.006065 44.3434
BM3D 0.0020406 53.8048
Figure 5: Comparison of denosing techniques for the phantom image: a) Original image b) Noisy image
c) sparsed noisy image d) denosing using BM3D e) denosing using LMMSE f) denosing using LASSO g)
denosing using Clustered LASSO.
In addition for the first set of synthetic data we have compared the different denoising techniques
using PSNR versus measurement ratio (M/N) and the result is shown in figure 7. Generally, the
CS based denosing performs well in relation to these metrics if we have a sparse and clustered
image.
11. Computer Science & Information Technology (CS & IT) 195
Figure 6 Comparison of denosing (reconstruction) algorithms using PSNR versus measurement ration M/N.
5. CONCLUSIONS
In this paper, denosing using compressive sensing under Bayesian framework is presented. Our
emphasis in this work is to incorporate prior information’s in the denosing of images with further
intention to apply such techniques to medical imaging, which usually have sparse, and some
clustredness characteristics. The denosing procedure in this work is done simultaneously with the
reconstruction of the signal, which is an advantage from the traditional denosing procedures.
Since using CS basically has already additional advantage of recovering images from under
sampled data using fewer measurements! We showed also that clustered LASSO denosing does
well for different noise models. In addition, in this work we have shown comparison of the
different reconstruction algorithms performance for different amount of measurement versus
PSNR. For future work we plan to apply different forms of clustering depending on the prior
information’s of images or geometry of clustredness.
ACKNOWLEDGEMENTS
We are grateful to Lars Lundheim for interesting discussions and suggestions.
REFERENCES
[1] S Preethi and D Narmadha. Article: A Survey on Image Denoising Techniques. International Journal
of Computer Applications 58(6):27-30, November 2012.
[2] Wonseok Kang ; Eunsung Lee ; Sangjin Kim ; Doochun Seo ; Joonki Paik; Compressive sensing-
based image denoising using adaptive multiple samplings and reconstruction error control . Proc.
SPIE 8365, Compres- sive Sensing, 83650Y (June 8, 2012);
[3] Jin Quan; Wee, W.G.; Han, C.Y., ”A New Wavelet Based Image De- noising Method,” Data
Compression Conference (DCC), 2012 , vol., no., pp.408,408, 10-12 April 2012.
[4] D. Donoho Compressed sensing, IEEE Trans. Inform. Theory 52 (4) (2006), pp. 12891306.
[5] Emmanuel J. Candes and Terence Tao, Decoding by linear programming IEEE TRANSACTIONS
ON INFORMATION THEORY, VOL. 51, NO. 12, DECEMBER 2005.
12. 196 Computer Science & Information Technology (CS & IT)
[6] E. Cand‘es, J. Romberg, and T. Tao, Robust uncertainty principles: Ex- act signal reconstruction from
highly incomplete frequency information, IEEE Trans. Inform. Theory, vol. 52, no. 2, pp. 489509,
Feb. 2006.
[7] E. J. Cande‘s and T. Tao, Near-optimal signal recovery from random projections: Universal encoding
strategies?, IEEE Trans. Inf. Theory, vol. 52, pp. 54065425, Dec. 2006.
[8] Michael Lustig and David Donoho and John M. Pauly, Sparse MRI: The Application of Compressed
Sensing for Rapid MR Imaging SPARS’09 Signal Processing with Adaptive Sparse Structured
Representations inria- 00369642, version 1 (2009).
[9] Marcio M. Marim, Elsa D. Angelini, Jean-Christophe Olivo-Marin, A Compressed Sensing Approach
for Biological Microscopy Image Denoising IEEE Transactions 2007.
[10] Wonseok Kang; Eunsung Lee;Eunjung Chea; Katsaggelos, A.K.; Joonki Paik, Compressive sensing-
based image denoising using adaptive multiple sampling and optimal error tolerance Acoustics,
Speech and Signal Processing (ICASSP), 2013 IEEE International Conference on , vol., no.,
pp.2503,2507, 26-31 May 2013.
[11] E.T. Jaynes, Probability Theory, The Logic of Science, Cambridge University Press., ISBN:. 2003.
[12] David J.C. Mackay Information Theory, Inference, and Learning Algorithms, Cambridge University
Press., ISBN: 978-0-521-64298-9, 2003.
[13] Anthony O’Hagen and Jonathan Forster, Kendall’s Advanced Theory of statistics, volume 2B,,
Bayesian Inference, Arnold, a member of the Hodder Headline Group ,ISBN: 0 340 807520, 2004.
[14] James O. Berger Bayesian and Conditional Frequentist Hypothesis Testing and Model Selection, VIII
C:L:A:P:E:M: La Havana, Cuba, November 2001.
[15] Bradley Efron, Modern Science and the Bayesian-Frequentist Controversy; 2005-19B/233, January,
2005.
[16] Michiel Botje R.A.Fisher on Bayes and Bayes’ Theorem ,Bayesian Analysis ,2008.
[17] Elias Moreno and F. Javier Giron, On the Frequentist and Bayesian approaches to hypothesis testing .
January-June 2006,3-28.
[18] Lei Yu, Hong Sun, Jean Pierre Barbot, Gang Zheng, Bayesian Compressive Sensing for clustered
sparse signals IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP),
2011.
[19] K.J. Friston, W. Penny, C. Phillips, S. Kiebel, G. Hinton, J. Ashburner, Classical and Bayesian
Inference in Neuroimaging: Theory Neuro Image, Volume 16, Issue 2, Pages 465 483 June 2002.
[20] Solomon A. Tesfamicael and Faraz Barzideh, Clustered Compressed Sensing in fMRI Data Analysis
Using a Bayesian Framework, International Journal of Information and Electronics Engineering vol.
4, no. 2, pp. 74-80, 2014.
[21] Dharmpal D. Doye and Sachin D Ruikarh, Wavelet Based Image Denoising Technique, International
Journal of Advanced Computer Science and Applications IJACSA (2011).
[22] Amin Tavakoli and Ali Pourmohammad, Image Denoising Based on Compressed Sensing,
International Journal of Computer Theory and Engineering vol. 4, no. 2, pp. 266-269, 2012.
[23] S. Rangan, A. K. Fletcher, and V. K. Goyal, Asymptotic analysis of MAP estimation via the replica
method and applications to compressed sensing, arXiv:0906.3234v1, 2009.
[24] Mark Schmidt, Least Squares Optimization with L1-Norm Regularization 2005.
[25] Robert Tibshirani, Regression shrinkage and selection via the lasso, In Journal of the Royal Statistical
Society, Series B, volume 58, pages 267288, 1994.
[26] Dabov, K.; Foi, A.; Katkovnik, V.; Egiazarian, K., Image Denoising by Sparse 3-D Transform
Domain Collaborative Filtering Image Processing, IEEE Transactions on , vol.16, no.8, pp.2080,2095,
Aug. 2007.
13. Computer Science & Information Technology (CS & IT) 197
AUTHORS
Solomon A. Tesfamicael was born in Gonder, Ethiopia in 1973. He received his
Bachelor degree in Mathematics from Bahirdar university, Bahirdar, Ethiopia in 2000
and Master degree in Coding theory from the Norwegian University of Science and
Technology (NTNU) in Trondheim, Norway in 2004. He began his PhD studies in
signal processing sept, 2009 at the department of Electronics and Telecomunications at
NTNU. He is currently working as LECTURER at the Sør-Trondlag university collge
(HiST), in Trondheim, Norway. He has worked as mathematics teacher for secondary schools and as
assistant LECTURER at the Engineering faculity in Bahirdar university in Ethiopia. In addition, he has a
pedagogical studies both in Ethiopia and in Norway. He has authored and co-authtored papers related to
compressed sensing (CS) and multiple input and multiple out put (MIMO) systems. His research interest
are signal processing, Compresses sensing, multiuser communication (MIMO, CDMA), statistical
mechanical methods like replica method, functional magnetic resonance imaging (fMRI) and
mathematical education.
Faraz Barzideh was born in Tehran, Iran in 1987. He received his bachelor degree from
Zanjan University, Zanjan, Iran, in the field of Electronic Engineering in 2011 and
finished his master degree in the field of Medical Signal Processing and Imaging from
Norwegian University of Science and Technology (NTNU) in 2013 and started his PhD
study in University of Stavanger (UiS) in 2014. His research interests are medical signal
and image processing especially in MRI and also compressive sensing and dictionary
learning.