This document discusses image restoration techniques. It compares the Wiener filter and Lucy-Richardson algorithm for restoring blurred and noisy images. The Structural Similarity Index Method (SSIM) is used to evaluate which technique produces better results. The experiments found that the Wiener filter performed better in cases with higher noise levels, while the Lucy-Richardson algorithm worked better with limited noise. The document also provides background on image degradation models, point spread functions, and the different approaches used by the Wiener filter and Lucy-Richardson algorithm.

1. Samer Mahmoud Shorman
USIM

2. Introduction
Image Restoration Model
Lucy-Richardson Algorithm
Wiener Filter Technique
Structural Similarity Index Method(SSIM)
Point Spread Function(PSF)
Experiment Results
Conclusion

3. Image restoration aims to recover an
original image from the degraded
image that was affected by blurring
and noise.
The degrading process is formulated by
a Point Spread Function (PSF) with an
original image and noise.
The results from blurred image, it is
affecting identification and extraction of
the useful information in the images.

4. We compared two methods which are Wiener
filter and Richardson Lucy.
The novelty in this experiment will be using
Structural Similarity Index Method (SSIM) in
order to distinguish which method had a
better accuracy.
The experiment result demonstrated
advantage for Wiener filter in higher noise
case.

5. h(x, y) n(x,y)
PSF
f(x, y) *
+
Degradation Image
g(x,y)
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.

6. Norbert Wiener proposed optimal filter called
Wiener filter which is:
A) An efficient method for restoration of
degraded image because it minimizes the
mean square error between the estimated
random process
B) Wiener filter assume, noise has zero mean,
and degradation function is known.
Note: The main disadvantage of Weiner filter
is that it cannot handle noises

7. The Lucy and Richardson proposed this algorithm
which is:
A) An iterative non-linear restoration method
B) Number of iterations to end the algorithm is
important
C) A good solution depends on the PSF
Note: As well as, increasing the number
of iterations not only slow down the
computational process, but also magnifies
noise and introduces waves near sharp
edges which called ringing effect

8. Proposed by Zhou Wang and others in
2004, which considers a full reference
metric that measurement is based on
an initially distortion-free image as
reference.
The experiments showed that it
compares favorably with other
methods such as MSE or PNSR.

9. PSF is known in advance from a blurred
image and it is an ill-posed problem
(unstable with respect to measurement
errors) due to the loss of information during
blurring, the problem with blind
deconvolution of recovering a blurry image
when the blur function is unknown
This kind of an algorithm to restore an
original image is requiring estimating a PSF

12. Image blur by motion blur and Gaussian noise

14. Analysis result: The Wiener introduces
better result with increasing noise.

15. This paper compares between two techniques,
which are Wiener filter and Lucy-Richardson,
using measurement metrics MSE, PSNR, and
SSIM. The result shows SSIM is complementary
to the conventional approaches.
The experiment shows fluctuation race
between methods, the result of SSIM
introduces advantage to Wiener in higher noise
case and advantage to Lucy-Richardson with
limited noise level.