On Comparative study of Image Restoration Algorithms

Comparative Study of Image Restoration Algorithm
Faizan Abbas Ali (EE10B081)
Under the guidance of Dr. Aravind R.
Department of Electrical Engineering
IIT Madras
May 15, 2015
Faizan Abbas Ali Comparative Study of Image Restoration Algorithm

Outline
Ÿ Introduction
Ÿ Image Restoration Techniques
Ÿ Results and Discussion

Outline
Ÿ Introduction
Ÿ Motivation
Ÿ State of Art

Outline
Ÿ Introduction
Ÿ Motivation
Ÿ State of Art
Ÿ Optimization Methods
Ÿ Wiener Filtering
Ÿ Bayesian Image Restoration

Outline
Ÿ Introduction
Ÿ Motivation
Ÿ State of Art
Ÿ Optimization Methods
Ÿ Wiener Filtering
Ÿ Bayesian Image Restoration
Ÿ Convergence of Richardson-Lucy algorithm
Ÿ C++ Implementation of Richardson-Lucy algorithm

Introduction
What is Image Restoration?
Ÿ Recovering true image from degraded image

Introduction
Scope and why is it Interesting?
Ÿ Surveillance

Introduction
Ÿ Surveillance
Ÿ Out-of-Focus Images

Introduction
Ÿ Surveillance
Ÿ Out-of-Focus Images
Ÿ Remote Sensing

Introduction
State-of-Art

Introduction
State-of-Art
Ÿ Classication
Ÿ Assumptions

Introduction
State-of-Art
Ÿ Classication
Ÿ non-blind de-convolution
Ÿ blind de-convolution
Ÿ Assumptions
Ÿ Linear shift invariant blur degradation model

Optimization Algorithm

Least Square Estimation
ˆf arg minf ||g¡Hf||2 H g

Least Square Estimation
ˆf arg minf ||g¡Hf||2 H g
Steepest Descent and Conjugate Gradient Algorithms
Ÿ f pi 1qpx, yq
f piqpx, yq αhT px, yq¦pgpx, yq¡hpx, yq¦f piqpx, yqq
Ÿ Conjugate gradient searches for minima in opposite direction
of gradient

Image Restoration
Wiener Filtering

Image Restoration
Wiener Filtering
W pu, vq H¦pu,vq
|Hpu,vq|2 Snpu,vq
Sf pu,vq

Image Restoration
Wiener Filtering
W pu, vq H¦pu,vq
|Hpu,vq|2 Snpu,vq
Sf pu,vq
Pseudo-code
for k Ñ 0 to 2 do
calculate ˆH H¦
H2 k
calculate estimate ˆF ˆHG
nd ˆF such that
b
|F ¡ ˆF|2 is minimum
output ˆF
end for

Image Restoration
Wiener Filtering of SIV gaussian blurred images with added WGN
σb 0.5 σn 15 σb 1.2 σn 15

Bayesian Image Restoration - Richardson-Lucy Algorithm
Richardson-Lucy Algorithm
f pi 1qpx, yq

gpx,yq
hpx,yq¦f piqpx,yq ¦hT px, yq

¦f piqpx, yq
Pseudo-code
degraded image g and kernel k
initial estimate f0 g
k
input number of iteration n
for iteration 1 to n do
Subtract from blurred image b g ¡fi
k
Add the error corrected image a b fi
Set image for next iteration fi a
end for

Explanation of deconvlucy MATLAB
Ÿ Parameters
Ÿ NUMIT
Ÿ READOUT
Ÿ SUBSMPL
Ÿ Preprocessing of inputs
Ÿ L-R iterations
Ÿ Error correction matrix and positivity constraints
Ÿ Convolving error corrected matrix with blur kernel
Ÿ Calling corelucy
Ÿ Setting next - previous

Explanation of deconvlucy MATLAB contd...
Ÿ corelucy
Ÿ Convolving input with the blur kernel
Ÿ Reshape on number of non-singleton dimensions
Ÿ Estimating image for next iteration

Convergence of RL algorithm
Figure: MSE error of an estimated
image and original image vs log of
iteration of RL algorithm performed
Ÿ grayscale images were used
Ÿ SIV blurring with added
WGN
Ÿ non-blind deconvolution
performed
Ÿ Algorithm is diverging
Ÿ deconvlucy MATLAB and our
implementation performed
identically

Convergence of RL algorithm contd...
Ÿ Comparison of performance of RL algorithm
Ÿ Grayscale images SIV blurred and noisy

Comparison of deconvlucy for blind and non-blind deconvolution
Ÿ Only blurred images converges at around 10 iterations
Ÿ Divergent behavior of RL algorithm due to noise

Comparison of deconvlucy for blind and non-blind deconvolution

Comparison of deconvlucy and our implementation for blind deconvolution

Comparison of deconvlucy and our implementation
for blind and non-blind deconvolution
using SSIM index

C++ implementation of RL algorithm
Ÿ opencv image processing modules used
Ÿ IplImage matrices used
Ÿ Cross-platform compatibility code
Ÿ opencv functions used

Ÿ IplImage matrices used
Ÿ Cross-platform compatibility code
Ÿ cvFilter2d
Ÿ cvCreateImage
Ÿ cvSub and cvAdd

True Image
C++ implementation output
Motion Blurred Image
deconvlucy output

True Image
C++ implementation output
Blurred Image
deconvlucy output ]

C++ Implementation of Super-resolution
Ÿ Working output from MATLAB C coder not obtained
Ÿ Modules implemented
Ÿ header.h
Ÿ params.h
Ÿ imLapband.cpp
Ÿ imagePatches.cpp
Ÿ DataGenerate.cpp
Ÿ ImageLumChrom.cpp
Ÿ test2Patches.cpp
Ÿ superResolvingAlgo.cpp

C++ Implementation of Super-resolution
Ÿ cvtColor
Ÿ split
Ÿ merge
Ÿ GaussianBlur
Ÿ clone
Ÿ add
Ÿ subtract
Ÿ size
Ÿ Filter2d
Ÿ Implementation issue faced
Ÿ cvMat data type was used
Ÿ meshgrid was implemented using nested for loops

Conclusion
Ÿ blind and non-blind image restoration algorithms were
reviewed
Ÿ Richardson-Lucy algorithm was studied in-depth
Ÿ Convergence of Richardson-Lucy algorithm was analyzed
Ÿ Performance of C++ implementation and deconvlucy was
compared
Ÿ Super-resolution algorithm was implemented in C++

References
W. H. Richardson, Bayesian-based iterative method of image
restoration, Journal of the Optical Society of America, vol. 62,
pp. 5559, January 1972.
L. B. Lucy, An iteration technique for the rectication of the
obscured distribution, The Astronomical Journal, vol. 79,
pp. 745754, June 1974.
D. S. C. Biggs and M. Andrews, Acceleration of iterative
image restoration algorithms, Applied Optics, vol. 36, no. 8,
pp. 17661775, 1997.
H. Bi and G. Boerner, When does the Richardson-Lucy
deconvolution converge?, Astronomy and Astrophysics Suppl.,
vol. 108, pp. 409415, Dec. 1994.

On Comparative study of Image Restoration Algorithms

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