This document discusses image restoration techniques. It describes how image degradation occurs through various processes and the goal of image restoration is to reconstruct the original image from its degraded version. There are two main categories of restoration techniques - deterministic and stochastic. Deterministic techniques use an inverse transformation when the degradation function is known, while stochastic techniques estimate the best restoration according to some criterion. Common degradation functions include relative motion, lens focus issues, and atmospheric turbulence. Inverse filtration and Wiener filtration are two restoration methods described, with Wiener filtration taking noise into account to minimize mean square error.
In the past two decades, the technique of image processing has made its way into every aspect of today’s tech-savvy society. Its applications encompass a wide variety of specialized disciplines including medical imaging, machine vision, remote sensing and astronomy. Personal images captured by various digital cameras can easily be manipulated by a variety of dedicated image processing algorithms. Image restoration can be described as an important part of image processing technique. The basic objective is to enhance the quality of an image by removing defects and make it look pleasing. The method used to carry out the project was MATLAB software. Mathematical algorithms were programmed and tested for the result to find the necessary output. In this project mathematical analysis was the basic core. Generally the spatial and frequency domain methods were both important and applicable in different technologies. This project has tried to show the comparison between spatial and frequency domain approaches and their advantages and disadvantages. This project also suggested that more research have to be done in many other image processing applications to show the importance of those methods.
In the past two decades, the technique of image processing has made its way into every aspect of today’s tech-savvy society. Its applications encompass a wide variety of specialized disciplines including medical imaging, machine vision, remote sensing and astronomy. Personal images captured by various digital cameras can easily be manipulated by a variety of dedicated image processing algorithms. Image restoration can be described as an important part of image processing technique. The basic objective is to enhance the quality of an image by removing defects and make it look pleasing. The method used to carry out the project was MATLAB software. Mathematical algorithms were programmed and tested for the result to find the necessary output. In this project mathematical analysis was the basic core. Generally the spatial and frequency domain methods were both important and applicable in different technologies. This project has tried to show the comparison between spatial and frequency domain approaches and their advantages and disadvantages. This project also suggested that more research have to be done in many other image processing applications to show the importance of those methods.
Basic Introduction about Image Restoration (Order Statistics Filters)
Median Filter
Max and Min Filter
MidPoint Filter
Alpha-trimmed Mean filter.
and Brief Introduction to Periodic Noise
Any Question contact kalyan.acharjya@gmail.com
Image Acquisition and Representation
A Simple Image Formation Model
Image Sampling and Quantization
Image Interpolation
Image quantization
Nearest Neighbor Interpolation
This is the basic introductory presentation for beginners. It gives you the idea about what is image processing means. The presentation consists of introduction to digital image processing, image enhancement, image filtering, finding an image edge, image analysis, tools for image processing and finally some application of digital image processing.
At the end of this lesson, you should be able to;
describe Connected Components and Contours in image segmentation.
discuss region based segmentation method.
discuss Region Growing segmentation technique.
discuss Morphological Watersheds segmentation.
discuss Model Based Segmentation.
discuss Motion Segmentation.
implement connected components, flood fill, watershed, template matching and frame difference techniques.
formulate possible mechanisms to propose segmentation methods to solve problems.
An introduction to Digital Image Processing as a continuation of a classic Digital Signal Processing course delivered at the University of Plymouth (2011)
Speckle Noise Reduction in Ultrasound Images using Adaptive and Anisotropic D...Md. Shohel Rana
US Imaging Technique less cost. Nonlinear and Anisotropic filter for removing speckle noise can be removed from US images. Proposed a modified Anisotropic filter which reduces speckle noises.
Computer Vision: Correlation, Convolution, and GradientAhmed Gad
Three important operations in computer vision are explained starting with each one got explained and implemented in Python.
Generally, all of these three operations have many similarities in as they follow the same general steps but there are some subtle changes. The main change is using different masks.
This slides about brief Introduction to Image Restoration Techniques. How to estimate the degradation function, noise models and its probability density functions.
Basic Introduction about Image Restoration (Order Statistics Filters)
Median Filter
Max and Min Filter
MidPoint Filter
Alpha-trimmed Mean filter.
and Brief Introduction to Periodic Noise
Any Question contact kalyan.acharjya@gmail.com
Image Acquisition and Representation
A Simple Image Formation Model
Image Sampling and Quantization
Image Interpolation
Image quantization
Nearest Neighbor Interpolation
This is the basic introductory presentation for beginners. It gives you the idea about what is image processing means. The presentation consists of introduction to digital image processing, image enhancement, image filtering, finding an image edge, image analysis, tools for image processing and finally some application of digital image processing.
At the end of this lesson, you should be able to;
describe Connected Components and Contours in image segmentation.
discuss region based segmentation method.
discuss Region Growing segmentation technique.
discuss Morphological Watersheds segmentation.
discuss Model Based Segmentation.
discuss Motion Segmentation.
implement connected components, flood fill, watershed, template matching and frame difference techniques.
formulate possible mechanisms to propose segmentation methods to solve problems.
An introduction to Digital Image Processing as a continuation of a classic Digital Signal Processing course delivered at the University of Plymouth (2011)
Speckle Noise Reduction in Ultrasound Images using Adaptive and Anisotropic D...Md. Shohel Rana
US Imaging Technique less cost. Nonlinear and Anisotropic filter for removing speckle noise can be removed from US images. Proposed a modified Anisotropic filter which reduces speckle noises.
Computer Vision: Correlation, Convolution, and GradientAhmed Gad
Three important operations in computer vision are explained starting with each one got explained and implemented in Python.
Generally, all of these three operations have many similarities in as they follow the same general steps but there are some subtle changes. The main change is using different masks.
This slides about brief Introduction to Image Restoration Techniques. How to estimate the degradation function, noise models and its probability density functions.
This presentation contains concepts of different image restoration and reconstruction techniques used nowadays in the field of digital image processing. Slides are prepared from Gonzalez book and Pratt book.
Non-Blind Deblurring Using Partial Differential Equation MethodEditor IJCATR
In this paper, a new idea for two dimensional image deblurring algorithm is introduced which uses basic concepts of PDEs... The various methods to estimate the degradation function (PSF is known in prior called non-blind deblurring) for use in restoration are observation, experimentation and mathematical modeling. Here, PDE based mathematical modeling is proposed to model the degradation and recovery process. Several restoration methods such as Weiner Filtering, Inverse Filtering [1], Constrained Least Squares, and Lucy -Richardson iteration remove the motion blur either using Fourier Transformation in frequency domain or by using optimization techniques. The main difficulty with these methods is to estimate the deviation of the restored image from the original image at individual points that is due to the mechanism of these methods as processing in frequency domain .Another method, the travelling wave de-blurring method is a approach that works in spatial domain.PDE type of observation model describes well several physical mechanisms, such as relative motion between the camera and the subject (motion blur), bad focusing (defocusing blur), or a number of other mechanisms which are well modeled by a convolution. In last PDE method is compared with the existing restoration techniques such as weiner filters, median filters [2] and the results are compared on the basis of calculated PSNR for various noises
This paper presents a frequency domain degraded
image restoration practical method. We call it practical wiener
filter. Using this filter, the value for K parameter of wiener
filter is determined experimentally that is so difficult and
time consuming. Furthermore, there is no any absolute remark
to claim that the obtained images by restoration process are
the best could be possible. In order to find a solution for this
problem, we use genetic algorithm to obtain the best value for
K. Therefore, this paper presents an image restoration method
which employs a Computer Aided Design (CAD) to image
restoration where there is no need to original safe image. It
means that, degraded image is as input and restored one is as
output of CAD. Simulation results confirm that this method
is successful and has executive ability in most applications.
Parametric Blur Estimation Using Modified Radon Transform for Natural Images Restoration Vedhapriya Vadhana R – Associate Professor,
Department of ECE,
Maheswari E – PG scholar,
VLSI DESIGN,
Francis Xavier Engineering College, Tirunelveli,India
Advance in Image and Audio Restoration and their Assessments: A ReviewIJCSES Journal
Image restoration is the process of restoring the original image from a degraded one. Images can be affected by various types of noise, such as Gaussian noise, impulse noise, and affected by blurring, which is happened during image recordings like motion blur, Out-of-Focus Blur, and others. Image restoration techniques are used to reverse the effect of noise and blurring. Restoration of distorted images can be done using some information about noise and the blurring nature or without any knowledge about the image degradation process. Researchers have proposed many algorithms in this regard; in this paper, different noise and degradation models and restoration methods will be discussed and review some researches in this field.
2. Imagerestoration - suppressing image
degradation using knowledge about its nature
3. Image restoration as inverse
convolution of the whole image
Most image restoration methods are based on
convolution applied globally to the whole image.
Degradation causes:
defects of optical lenses,
nonlinearity of the electro-optical sensor,
graininess of the film material,
relative motion between an object and camera
wrong focus,
atmospheric turbulence in remote sensing or astronomy,
etc.
4. Theobjective of image restoration is to
reconstruct the original image from its
degraded version.
Image restoration techniques - two groups:
5. Deterministic methods - applicable to images with
little noise and a known degradation function.
The original image is obtained from the degraded one by a
transformation inverse to the degradation.
Stochastic techniques - the best restoration is
sought according to some stochastic criterion, e.g.,
a least squares method.
In some cases the degradation transformation must be
estimated first.
6. It is advantageous to know the degradation function
explicitly.
The better this knowledge is, the better are the
results of the restoration.
There are three typical degradations with a simple
function:
Relative constant speed movement of the object with
respect to the camera,
wrong lens focus,
and atmospheric turbulence.
7. Inmost practical cases, there is insufficient
knowledge about the degradation, and it must
be estimated and modeled.
8. Methods:
A priori knowledge about degradation - either known in
advance or obtained before restoration.
If it is clear in advance that the image was degraded by
relative motion of an object with respect to the sensor then
the modeling only determines the speed and direction of
the motion.
An example of parameters obtained before
restoration is an attempt to estimate parameters of a
capturing device such as a TV camera or digitizer.
9. A posteriori knowledge is obtained by analyzing
the degraded image.
A typical example is to find some interest points in
the image (e.g. corners, straight lines) and guess
how they looked before degradation.
Another possibility is to use spectral characteristics
of the regions in the image that are relatively
homogeneous.
10. A degraded image g can arise from the
original image f by a process which can be
expressed as
where s is some nonlinear function and nu
describes the noise.
11. The degradation is very often simplified by
neglecting the nonlinearity
assuming that the function h is invariant with
respect to position in the image.
Degradation can be then expressed as
convolution
12. Ifthe degradation is given by above equation
and the noise is not significant then image
restoration equates to inverse convolution
(also called deconvolution).
Ifnoise is not negligible then the inverse
convolution is solved as an overdetermined
system of linear equations.
13. Degradations that are
easy to restore
Some degradations can be easily expressed
mathematically (convolution) and also
restored simply in images.
TheFourier transform H of the convolution
function is used.
14. Relative motion of
the camera and object
Assume an image is acquired with a camera
with a mechanical shutter.
Relativemotion of the camera and the
photographed object during the shutter open
time T causes smoothing of the object in the
image.
15. Suppose V is the constant speed in the
direction of the x axis; the Fourier transform
H(u,v) of the degradation caused in time T is
given by
16. Wrong lens focus
Image smoothing caused by imperfect focus
of a thin lens can be described by the
following function
where J1 is the Bessel function of the first
order, r2 = u2 + v2, and a is the displacement.
17. Atmospheric turbulence
needs to be restored in remote sensing and
astronomy
caused by temperature non-homogeneity in the
atmosphere that deviates passing light rays.
The mathematical model
where c is a constant that depends on the type of
turbulence which is usually found experimentally. The
power 5/6 is sometimes replaced by 1.
18. Inverse filtration
based on the assumption that degradation
was caused by a linear function h(i,j)
theadditive noise nu is another source of
degradation.
Itis further assumed that nu is independent
of the signal.
19. Applying the Fourier transform
The degradation can be eliminated if the
restoration filter has a transfer function that is
inverse to the degradation h ... or in Fourier
transform H-1(u,v).
20. Theundegraded image F is derived from its
degraded version G.
Thisequation shows that inverse filtration
works well for images that are not corrupted
by noise.
21. If noise is present and additive error occurs, its
influence is significant for frequencies where H(u,v)
has small magnitude. These usually correspond to
high frequencies u,v and thus fine details are blurred
in the image.
The changing level of noise may cause problems as
well because small magnitudes of H(u,v) can cause
large changes in the result.
Inverse filter values should not be of zero value so
as to avoid zero divides in above equation.
22. Wiener filtration
Itis no surprise that inverse filtration gives
poor results in pixels suffering from noise
since the noise is not taken into account.
Wiener filtration explores a priori knowledge
about the noise.
23. Restoration by the Wiener filter gives an
estimate of the original uncorrupted image f
with minimal mean square error e2
24. No constraints applied to above equation
optimal estimate ^f is the conditional mean value
of the ideal image f under the condition g
complicated from the computational point of view
also, the conditional probability density between
the optimal image f and the corrupted image g is
not usually known.
the optimal estimate is in general a nonlinear
function of the image g.
25. Minimization of e2 is easy if estimate ^f is a
linear combination of the values in the image
g -close-optimal solution
H ... Fourier transform of the Wiener filter -
W
considers noise - see Eq. below
G ... Fourier transform of the degraded image
26. Where,
H is the transform function of the degradation
# denotes complex conjugate
S_{nu nu} is the spectral density of the noise
S_{gg} is the spectral density of the degraded
image
27. If Wiener filtration is used, the nature of degradation
H and statistical parameters of the noise need to be
known.
Wiener filtration theory solves the problem of a
posteriori linear mean square estimate -- all statistics
(e.g., power spectrum) should be available in
advance.
Note that the inverse filter discussed earlier is a
special case of the Wiener filter where noise is
absent i.e. S_{nu nu} = 0.