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

� Introduction

� Motivation� State of Art

� Image Restoration Techniques

� Optimization Methods� Wiener Filtering� Bayesian Image Restoration

� Results and Discussion

� Convergence of Richardson-Lucy algorithm� C++ Implementation of Richardson-Lucy algorithm


Outline

� Introduction� Motivation� State of Art

� Image Restoration Techniques

� Optimization Methods� Wiener Filtering� Bayesian Image Restoration




Outline


� Image Restoration Techniques� Optimization Methods� Wiener Filtering� Bayesian Image Restoration




Outline


� Image Restoration Techniques� Optimization Methods� Wiener Filtering� Bayesian Image Restoration

� Results and Discussion� Convergence of Richardson-Lucy algorithm� C++ Implementation of Richardson-Lucy algorithm


Introduction

What is Image Restoration?

� Recovering true image from degraded image

Scope and why is it Interesting?� Surveillance

� Out-of-Focus Images

� Remote Sensing


Introduction

State-of-Art

� Classi�cation� non-blind de-convolution� blind de-convolution

� Assumptions

� Linear shift invariant blur degradation model


Introduction

State-of-Art� Classi�cation

� non-blind de-convolution� blind de-convolution

� Assumptions

� Linear shift invariant blur degradation model


Introduction

State-of-Art� Classi�cation

� non-blind de-convolution� blind de-convolution

� Assumptions� Linear shift invariant blur degradation model


Optimization Algorithm

Least Square Estimation

f � argminf ||g�Hf||2 � H�g

Steepest Descent and Conjugate Gradient Algorithms

� f pi�1qpx , yq �f piqpx , yq � αhT px , yq � pgpx , yq � hpx , yq � f piqpx , yqq

� Conjugate gradient searches for minima in opposite directionof gradient


Image Restoration

Wiener Filtering

W pu, vq � H�pu,vq

|Hpu,vq|2�Snpu,vqSf pu,vq

Pseudo-codefor k Ñ 0 to 2 do

calculate H � H�

H2�k

calculate estimate F � HG

�nd F such that

b|F � F |2 is minimum

output Fend 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 ,yqhpx ,yq�f piqpx ,yq

� hT px , yq�� f piqpx , yq

Pseudo-code

degraded image g and kernel kinitial estimate f0 � g kinput number of iteration nfor iteration 1 to n do

Subtract from blurred image b � g � fi kAdd the error corrected image a � b � fiSet image for next iteration fi � a

end for



Explanation of deconvlucy MATLAB

� Parameters� NUMIT� READOUT� SUBSMPL

� Preprocessing of inputs

� L-R iterations

� Error correction matrix and positivity constraints� Convolving error corrected matrix with blur kernel� Calling corelucy� Setting next -> previous



Explanation of deconvlucy MATLAB contd...

� corelucy

� Convolving input with the blur kernel� Reshape on number of non-singleton dimensions� 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

� grayscale images were used

� SIV blurring with addedWGN

� non-blind deconvolutionperformed

� Algorithm is diverging

� deconvlucy MATLAB and ourimplementation performedidentically



Convergence of RL algorithm contd...

� Comparison of performance of RL algorithm

� Grayscale images SIV blurred and noisy




Comparison of deconvlucy for blind and non-blind deconvolution

� Only blurred images converges at around 10 iterations

� 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 implementationfor blind and non-blind deconvolution

using SSIM index



C++ implementation of RL algorithm

� opencv image processing modules used

� IplImage matrices used

� Cross-platform compatibility code

� opencv functions used

� cvFilter2d� cvCreateImage� cvSub and cvAdd





� IplImage matrices used

� Cross-platform compatibility code

� opencv functions used� cvFilter2d� cvCreateImage� cvSub and cvAdd




True Image

C++ implementation output

Motion Blurred Image

deconvlucy outputFaizan Abbas Ali Comparative Study of Image Restoration Algorithm



True Image

C++ implementation output

Blurred Image

deconvlucy output ]Faizan Abbas Ali Comparative Study of Image Restoration Algorithm

C++ Implementation of Super-resolution

� Working output from MATLAB C coder not obtained


� Modules implemented� header.h� params.h� imLapband.cpp� imagePatches.cpp� DataGenerate.cpp� ImageLumChrom.cpp� test2Patches.cpp� superResolvingAlgo.cpp


C++ Implementation of Super-resolution

� opencv functions used� cvtColor� split� merge� GaussianBlur� clone� add� subtract� size� Filter2d

� Implementation issue faced� cvMat data type was used� meshgrid was implemented using nested for loops


Conclusion

� blind and non-blind image restoration algorithms werereviewed

� Richardson-Lucy algorithm was studied in-depth

� Convergence of Richardson-Lucy algorithm was analyzed

� Performance of C++ implementation and deconvlucy wascompared

� Super-resolution algorithm was implemented in C++


References

W. H. Richardson, �Bayesian-based iterative method of imagerestoration,� Journal of the Optical Society of America, vol. 62,pp. 55�59, January 1972.

L. B. Lucy, �An iteration technique for the recti�cation of theobscured distribution,� The Astronomical Journal, vol. 79,pp. 745�754, June 1974.

D. S. C. Biggs and M. Andrews, �Acceleration of iterativeimage restoration algorithms,� Applied Optics, vol. 36, no. 8,pp. 1766�1775, 1997.

H. Bi and G. Boerner, �When does the Richardson-Lucydeconvolution converge?,� Astronomy and Astrophysics Suppl.,vol. 108, pp. 409�415, Dec. 1994.


on comparative study of image restoration algorithms

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