Samer Mahmoud Shorman

USIM

Introduction

Image Restoration Model

Lucy-Richardson Algorithm

Wiener Filter Technique

Structural Similarity Index Method(SSIM)

Point Spread Function(PSF)

Experiment Results

Conclusion

Image restoration aims to recover anoriginal image from the degradedimage that was affected by blurringand noise.

The degrading process is formulated bya Point Spread Function (PSF) with anoriginal image and noise.

The results from blurred image, it isaffecting identification and extraction ofthe useful information in the images.

We compared two methods which are Wienerfilter and Richardson Lucy.

The novelty in this experiment will be usingStructural Similarity Index Method (SSIM) inorder to distinguish which method had abetter accuracy.

The experiment result demonstratedadvantage for Wiener filter in higher noisecase.

The image restoration model is represented by this equation:

g(x, y) = f (x, y) * h(x, y) + n (x, y) (1)

where

f(x, y) represents an original image,

h(x, y) the point spread function of the blur,

n(x, y) represents an additive noise,

g (x, y) is the degraded image.

f(x, y)+

n(x,y)h(x, y)

*Degradation Image

g(x,y)

PSF

Norbert Wiener proposed optimal filter calledWiener filter which is:

A) An efficient method for restoration ofdegraded image because it minimizes themean square error between the estimatedrandom process

B) Wiener filter assume, noise has zero mean,and degradation function is known.

Note: The main disadvantage of Weiner filteris that it cannot handle noises

The Lucy and Richardson proposed this algorithm which is:

A) An iterative non-linear restoration method

B) Number of iterations to end the algorithm isimportant

C) A good solution depends on the PSF

Note: As well as, increasing the numberof iterations not only slow down thecomputational process, but also magnifiesnoise and introduces waves near sharpedges which called ringing effect

Proposed by Zhou Wang and others in2004, which considers a full referencemetric that measurement is based onan initially distortion-free image asreference.

The experiments showed that itcompares favorably with othermethods such as MSE or PNSR.

PSF is known in advance from a blurredimage and it is an ill-posed problem(unstable with respect to measurementerrors) due to the loss of information duringblurring, the problem with blinddeconvolution of recovering a blurry imagewhen the blur function is unknown

This kind of an algorithm to restore anoriginal image is requiring estimating a PSF

Image blur by motion blur and Gaussian noise

Analysis result: The Wiener introducesbetter result with increasing noise.

This paper compares between two techniques,which are Wiener filter and Lucy-Richardson,using measurement metrics MSE, PSNR, andSSIM. The result shows SSIM is complementaryto the conventional approaches.

The experiment shows fluctuation racebetween methods, the result of SSIMintroduces advantage to Wiener in higher noisecase and advantage to Lucy-Richardson withlimited noise level.