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  1. 1. K. Prasanthi Jasmine, Dr. P. Rajesh Kumar, K. Naga Prakash/ International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue4, July-August 2012, pp.1949-1954 An Effective Technique To Compress Images Through Hybrid Wavelet-Ridgelet Transformation K. Prasanthi Jasmine, Dr. P. Rajesh Kumar, K. Naga Prakash Department of ECE, Vijaya Institute of Technology for Women, Vijayawada Associate Professor, Department of ECE, College of Engineering, Andhra University, VisakhapatnaAbstract In recent days, images play a vital role in Images [5]. Eliminating this redundancy is the basica wide range of applications. Some of the idea behind compression systems [4]. The processsignificant application fields such as medical, that achieves data reduction without losing the imageeducation, surveillance also utilize images. Images information is termed as image compression.are of large size and hence they are difficult to Specified channel bandwidths or storage needs andtransmit and store. Images need compression for maintaining the highest possible quality are theeffective transmission and storage. A wide of important components to compress data [6]range of compression techniques are available in Lossy and lossless are two types ofthe literature. Some of the techniques only compression techniques [7]. An exact reconstructioncompress the images by minimizing the size on of the original signal can be obtained using methodsdisk without loss of data. In this paper, a hybrid from the lossless family; however they do not realizecompression technique comprised of wavelet and low data rates. Conversely, an exact reconstruction isridgelet methods is used for compressing images. not achieved by lossy methods; however higherInitially, the image is denoised with a filter and compression ratios can be achieved [8]. Selection ofthen the denoised image is transformed utilizing the compression method, lossy or lossless isDiscrete Wavelet Transform (DWT). After that, application dependant [7]. A smaller number of bitsFinite Ridgelet Transform (FRT) is employed on are required for the representation of the coded imagethe obtained wavelet coefficients, and the compared to that required for the representation ofcompressed image of reduced size is obtained. For the original image and this reduces thedecompression the Inverse FRT is employed communication time or the used storage space [9].subsequent to the inverse DWT process and the Old methods of compression like Fourier Transform,original image is obtained without loss of data. Hadamard and Cosine Transform etc., do not satisfy these requirements because huge mean square errorKeywords:- compression, decompression, occurs between the original and the reconstructedGaussian Filter, Discrete Wavelet Transform images. The purpose is very efficiently served by the(DWT), Finite Ridgelet Transform (FRT) wavelet transform approach [10]. Multiresolution theory is a powerful1. INTRODUCTION approach for wavelets based signal processing and Digital images have emerged as a significant analysis [11]. Data is transformed into diversesource of knowledge in the contemporary world of frequency components, signifying each componentcommunication systems [1]. A single image can with a resolution that corresponds to its scale by thereplace thousands of words of information as stated mathematical function namely wavelets that areby the phrase “a picture is worth thousand words” defined over a finite interval and have an average[2]. Internet, police department, medical images, value of zero [12]. Wavelets are employed to diversedigital libraries etc., are some of the several factors of imaging informatics, such as imageapplications which use images [5]. The bit rate of a compression. A major application area for wavelets isdigital system is calculated by multiplying the image compression. Compression can also besampling rate with the number of bits in each sample. achieved on the wavelet coefficients, because theRedundancy is the difference between the original image can be signified by a linearinformation rate of a signal and its bit rate [4]. relationship of the wavelet basis functions [13]. A set Compression of the image data can be of sub images with different resolutions matchingachieved by removing the redundancy. Spatial different frequency bands is obtained byRedundancy i.e. correlation between neighboring decomposing the image using the wavelet transformpixel values and Spectral Redundancy i.e. correlation [14] [15]. Another transformation that can be utilizedbetween different color planes or spectral bands are is Ridgelet. Wavelets are excellent at signifying pointthe two types of redundancies that exist in still singularities and ridgelets signify line singularities [16]. Functions on continuous spaces that have 1949 | P a g e
  2. 2. K. Prasanthi Jasmine, Dr. P. Rajesh Kumar, K. Naga Prakash/ International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue4, July-August 2012, pp.1949-1954certain discontinuities along lines can be represented signatures in images for confirming the ownerin multiple scales using the Ridgelet transform [17]. identification and reducing unauthorized copying. They have included a fuzzy inference filter to select In this paper, we propose a hybrid technique the larger entropy of coefficients to embedwhich is a wavelet- ridgelet combination for the watermarks. Unlike most prior watermarkingcompression of images. Initially, the input image frameworks which entrench watermarks in thewhich is in the RGB colorspace is converted to the greater coefficients of inner coarser subbands, theirgrayscale image for compression. After that the proposed technique has been based on exploiting agrayscale image is denoised by processing using a context model and fuzzy inference filter forGaussian filter, because the noise may degrade the embedding watermarks in the greater-entropyquality of the image. After that the denoised image is coefficients of coarser DWT subbands. Transparencytransformed using DWT and then using FRT to and robustness to the common image-processingacquire the compressed image. Subsequent to this attacks for example smoothing, sharpening, andprocess the decompressed image is obtained by JPEG compression, have been achieved in theirapplying inverse FRT and inverse DWT in proposed techniques by permitting insertion ofsuccession on the transformed image. As a result of adaptive casting degree of watermarks. The approachthis process the decompressed image is obtained. The has not required the original host image to get backrest of the paper is organized as follows section 2 the watermarks from the watermarked image. Theirpresents a brief review of some of the existing works schemes have been shown to offer excellentin image compression. The proposed mechanism to outcomes in both image transparency and robustness.compress the image using hybrid technique is The transform selected for imagedetailed in section 3. Section 4 describes the results compression must obtain a resultant data set that isand discussion. Finally, the conclusions are summed smaller than the source data set in terms of size.up in section 5. Wavelet transforms and wavelet packet transform have materialized as well-liked techniques forII. Related Researches: A Review continuous and discrete time cases. Tripatjot Singh et A handful of recent researches are available al [21] have attempted to find out the most excellentin the literature. Picture archiving and wavelet for compressing the still image at a particularcommunication systems have been utilized for decomposition level using wavelet transforms andstoring majority of the image data in hospitals in wavelet packet transforms. For decomposition leveldigital form With the widespread digitization of data 2, Compression Ratio (CR) and Energy Ratio (ER)and the rising use of telemedicine, the requirement have been decided for dissimilar wavelets at differentfor data storage and bandwidth requirements have threshold values ranging from 5 to 100.been rising and lossy compression techniques have To accomplish image compression, wavelet-become important. In literature, the triumphant use of Modified Single Layer Linear Forward Only Counterthe wavelet transform in the field of image Propagation Network (MSLLFOCPN) technique hascompression has been widely studied. For medical been presented by Narayanan Sreekumar et al [22].image compression, the functioning of Bi-orthogonal Properties of localizing the global spatial andspline wavelet as an efficient mode has been frequency correlation have been inherited by theirinvestigated by Loganathan et al [18]. An technique from wavelets. Function approximationexperimental setup to evaluate the effectiveness of and prediction have been achieved using neuralmedical image compression by means of bi- networks. As a result of its better performanceorthogonal wavelet has been executed. The result of counter propagation network has been considered andthe experimental set up for several reconstruction and the research has allowed them to suggest a neuraldecomposition values has obtained a quite stable network architecture named single layer linearcompression ratio. counter propagation network (SLLC). The Mansi Kambli et al. [19] have proposed a combination of wavelet and SLLC network has beenframework which is a Modified Set Partitioning in experimented on many benchmark images and theHierarchical Tree with Run Length Encoding for experimental outcomes have shown improvement infingerprint image compression. Their Proposed picture quality, compression ratio and approximationmethod is superior because lots of images associated or prediction comparable to existing and traditionalto the fingerprint image have been retrieved. Their neural networks.proposed method has been shown to execute well incompression and decompression by a test conducted III. Proposed Methodon an image database of grayscale bitmap images. Nowadays, the impact of images in the realThe picture quality of fingerprint images has been world applications is more. The storage and thedetermined using both Peak Signal to noise ratio and transmission of images is the important oneMean Square Error. nowadays because of its advantages. Hence the Ming-Shing Hsieh [20] has proposed a compression of images are important whileDWT-based watermarking technique to embed transmission and storage. In this paper we propose a 1950 | P a g e
  3. 3. K. Prasanthi Jasmine, Dr. P. Rajesh Kumar, K. Naga Prakash/ International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue4, July-August 2012, pp.1949-1954 hybrid effective technique to compress the image in I r , I g and I b be the red, green and blue an effective manner without losing the data. Let I be the image of RGB colorspace with dimension contribution of the image I gy is the gray scale image of M N where obtained by the aforesaid equation which is the 0  m  M  1 0  n  N  1 which is to be Craig’s formula for RGB to gray color conversion. compressed. After the conversion of RGB to gray scale image I gy , it is applied with the Gaussian filter which is applied for the denoising process.  (u 2 v 2 ) Input image (RGB colorspace) f (u, v)  e 2 2 (2) Convert input image to grayscale Where image f (u , v) f g (u , v) Apply Gaussian filter to grayscale image  f u v (3) The eqn (2) and eqn (3) are the Gaussian filter which may utilized for the denoising process. Apply DWT on denoised This Gaussian filter returns a rotationally symmetric image Gaussian lowpass filter of size [u, v] with standard deviation sigma (positive). After denoising the image DWT coefficients obtained using the Gaussian filter the denoised image I de is Figure 1. Propose obtained. Subsequent to this process, the Discrete Wavelet Transform (DWT) which is discrete 2D Apply Finite Ridgelet wavelet transform. DWT is based on sub-band Transform coding is utilized to defer a fast computation of wavelet transform. DWT reduces the computational Compression time and resources required and it is easy to FRT coefficients implement this DWT. The following details the DWT obtained process on the images and the following eqn details the 2D DWT process. Compressed image Apply inverse Finite Ridgelet Transform Apply inverse DWT Decompressi on Decompressed image Figure 2 2D DWT for image Initially the image I is in RGB colorspace is k 1 converted to gray scale image in which the image is to be compressed. The following equation details the H t   I de2 x t * S t ( z ) t o conversion process of RGB colorspaced image to the gray scale image. (4) I gy  0.2989  I r  0.5870  I g  0.1140  I b k 1 Lt   I de2 x t * pt ( z ) t o (1) Here (5) 1951 | P a g e
  4. 4. K. Prasanthi Jasmine, Dr. P. Rajesh Kumar, K. Naga Prakash/ International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue4, July-August 2012, pp.1949-1954These are the high pass and low pass coefficients for standard images and the following results arethe 2D DWT transform and the DWT coefficient obtained for the proposed method that is shown  below.vector is Dco . Subsequent to this process the finiteridgelet transform is applied on these coefficients.After obtaining these coefficients the image is thenapplied with the finite ridgelet transform which isdetailed in the steps below Input: Dco DWT coefficient vector, number ofdecomposition levelOutput: Ridgelet coefficients, normalized mean valueSteps 1. Resize the vector to p p the prime number  2. Compute the mean  of Dco   3. Dco  Dco   Normalize the mean value   p *  Figure 3. Original image 4.  5. Compute the finite radon transform r 6. Apply wavelet transform on the radon  transform r Now the FRIT coefficients r has been obtained nowthe compressed image has been obtained. Fordecompression the image has been applied with the inverse finite ridgelet transform initially the r ofridgelet transform coefficient is applied with the inverse FRIT. In the inverse FRIT the r istransformed to the radon domain and then the inversefinite radon transform has been obtained for it.    Dco  Dco   /(sizeof (r )  1) (6) After that the inverse DWT has been applied Figure 4. DWT applied imagon the image to obtain the original image ofdecompressed in size without losing of data. Henceour proposed hybrid technique compresses the imagein an effective manner without degrading the imagequality.IV. Results and Discussion The proposed hybrid technique to compressthe image has been implemented in the workingplatform of MATLAB (version 7.10). Initially theimage is converted to the gray scale conversion andthen the image is denoised with the Gaussian filter.Then the DWT is applied on the denoised image thenthe finite ridgelet transform is applied on the obtained Figure 5 Decompressed imagecoefficients and then the compressed image appliedwith the inverse ridgelet transform and then theinverse DWT has been applied on the image. Theproposed hybrid techniques have been tested on the 1952 | P a g e
  5. 5. K. Prasanthi Jasmine, Dr. P. Rajesh Kumar, K. Naga Prakash/ International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue4, July-August 2012, pp.1949-1954 Figurre 7 Graph for proposed PSNR and ridgelet Input PSNR for PSNR for transform PSNRImage Proposed Ridgelet Method Transform Figure 3 shows the original image and the imageLena 38.29281 20.37056 Figure 4 shows the DWT applied image and theBaboon 33.38936 19.72939 figure 4 shows the decompressed image withoutCameraman 36.07291 15.15914 degrading the quality. Table 1. Shows the PSNRHouse 42.09413 18.02169 comparison table for the proposed hybrid techniqueBarbara 39.71284 19.58824 and the ridgelet transform and the corresponding graph is shown in the Figure 7. Table 2 shows theTable 1. PSNR comparison for proposed hybrid size comparison for the original image and themethod and the ridgelet transform applied image decompressed image. V.Conclusion: Input image Original Decompressed In this paper, an effective hybrid technique size size to compress the image by means of a hybridLena 9771 8867 combination of wavelet-ridgelet techniques isBaboon 16418 13753 proposed. Initially, the original RGB colorspacedCameraman 10057 9144 image is converted to the grayscale image and thenHouse 8089 7549 the image is denoised using the Gaussian filter.Barbara 10926 9144 Subsequently, the image is transformed first using DWT and then using FRT. Now the compressedTable 2 Size for original image and the decompressed image has been obtained and after that the inverseimage comparison FRT transform is applied. Then finally, the inverse DWT transform is applied and the decompressed 18000 image is obtained. 16000 14000 REFERENCES 12000 [1] Sachin P. Nanavati and Prasanta K. Size(bytes) 10000 8000 Panigrahi, "Wavelets: Applications to image 6000 compression-I", Resonance, Vol. 10, No. 2, original 4000 pp. 52-61, February 2005 2000 Decompress 0 [2] Kharate, Patil and Bhale, "Selection of Lena Baboon Cameraman House Barbara Mother Wavelet for Image Compression on Basis of Image", Journal of Multimedia, Images Vol. 2, No. 6, pp. 44-52, November 2007 [3] Muna F. Al-Sammraie and Faisal G. Khamis, “Adaptive Image Compression Based Wavelet Using Space-Frequency Segmentation”, Research Journal of AppliedFigure 6 Graph for decompressed image size and Sciences, Vol. 3, No. 6, pp. 421-430, 2008original image size of Original and decompressed [4] Othman O. Khalifa, Sering Habib Hardingimage and Aisha-Hassan A. Hashim, "Compression using Wavelet Transform", Signal Processing: An International Journal (SPIJ), Vol. 2, No. 5, pp. 17-26, October 2008 [5] Nikkoo Khalsa, Sarate and Ingole, "Factors Influencing the Image Compression of Artificial and Natural Image Using Wavelet Transform", International Journal of Engineering Science and Technology, Vol. 2, No. 11, pp. 6225-6233, 2010 [6] Arunapriya and KavithaDevi, "Improved Digital Image Compression using Modified Single Layer Linear Neural Networks", International Journal of Computer Applications, Vol. 10, No. 1, pp. 41-46, November 2010 1953 | P a g e
  6. 6. K. Prasanthi Jasmine, Dr. P. Rajesh Kumar, K. Naga Prakash/ International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue4, July-August 2012, pp.1949-1954[7] Ghrare, Mohd. Ali, Jumari and Ismail, "An Wavelet Transform, A Comparative Study", Efficient Low Complexity Lossless Coding ICGST, Vol.8, No.3, pp.25-34, October Algorithm for Medical Images", American 2008[1] Sachin P. Nanavati and Prasanta K. Journal of Applied Sciences, Vol. 6, No. 8, Panigrahi, "Wavelets: Applications to image pp. 1502-1508, 2009 compression-I", Resonance, Vol. 10, No. 2,[8] Vibha Aggarwal and Manjeet Singh Patterh, pp. 52-61, February 2005 "ECG Compression using Wavelet Packet, [18] Loganathan and Kumaraswamy, "Medical Cosine Packet and Wave Atom Image Compression Using Biorthogonal Transforms", International Journal of Spline Wavelet with Different Electronic Engineering Research, Vol. 1, Decomposition", International Journal on No. 3, pp. 259-268, 2009 Computer Science and Engineering, Vol. 2,[9] El-Taweel, Mohammed Helal and Sabri No. 9, pp. 3003-3006, 2010 Saraya, “Lossless Image Compression Using [19] Mansi Kambli and Shalini Bhatia, Wavelet and Vector Quantization”, Journal "Fingerprint Image Compression", of Mansoura University, Vol. 31, No. 3, International Journal of Engineering Science September 2006 and Technology, Vol. 2, No. 5, pp. 919-928,[10] Anuj Bhardwaj and Rashid Ali, "Image 2010 Compression Using Modified Fast Haar [20] Ming-Shing Hsieh, "Perceptual Copyright Wavelet Transform", World Applied Protection Using Multiresolution Wavelet- Sciences Journal, Vol. 7, No. 5, pp. 647-653, Based Watermarking and Fuzzy Logic", 2009 International Journal of Artificial[11] Hamed Vahdat Nejad and Hossein Deldari, Intelligence and Applications (IJAIA), Vol. "A Parallel Quadtree Approach for Image 1, No. 3, pp. 45-57, July 2010 Compression using Wavelets", World [21] Tripatjot Singh, Sanjeev Chopra, Academy of Science, Engineering and Harmanpreet Kaur and Amandeep Kaur, Technology, No. 21, pp. 130-133, "Image Compression using Wavelet and September 2006 Wavelet Packet Transformation",[12] Anoop Mathew and Bensiker Raja Singh, International Journal of Computer Science "Image Compression using Lifting Based and Technology, Vol. 1, No. 1, pp. 97-99, DWT", International Journal of Computers, September 2010 Information Technology and Engineering, [22] Narayanan Sreekumar and Santhosh Baboo, Vol. 2, pp. 27-31, January-June 2009 "A Novel Enhanced Neural Network Model[13] Venkatrama Phani Kumar, KVK Kishore for Image Compression Using Wavelet – and Hemantha Kumar, "Face Recognition MSLLFOCPN", International Journal of Using Wavelet Based Kernel Locally Computer Applications, Vol. 6, No. 5, pp. Discriminating Projection", International 25-30, September 2010 Journal of Computer Theory and Engineering, Vol. 2, No. 4, pp. 636-641, August 2010[14] Vipula Singh, Navin Rajpal and Srikanta Murthy, "An Algorithmic Approach for Efficient Image Compression using Neuro- Wavelet Model and Fuzzy Vector Quantization Technique", International Journal on Computer Science and Engineering, Vol. 2, No. 7, pp. 2366-2374, 2010[15] Veeraswamy and SrinivasKumar, "An Improved Wavelet based Image Compression Scheme and Oblivious Watermarking", International Journal of Computer Science and Network Security, Vol. 8, No. 4, pp. 170-177, April 2008[16] Joshi, Manthalkar and Joshi, "Color Image Compression Using Wavelet and Ridgelet Transform", In proceedings of Seventh International Conference on Information Technology, pp.1318-1321, 2010[17] Joshi, Manthalkar and Joshi, "Image Compression Using Curvelet, Ridgelet and 1954 | P a g e