RestoMMMG

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* author: Emilie Chouzenoux       		      *
* institution: LIGM -  Universite de Marne la Vallee  *
* date: Wednesday, August 8th 2011   	              *
* License CeCILL-B                                    *
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* RECOMMENDATIONS:                                  *
* This toolbox is designed to work with             *
* Matlab 7.0                                        *
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DESCRIPTION:
This toolbox allows to restore an image degraded by a linear operator 
and Gaussian noise. The considered criterion is composed with 
-> a least square function as data fidelity term
J(x) = 1/2 || H(x)- y ||^2
-> a quadratic distance function allowing to constraint the dynamic range 
of the restored image into [xmin,xmax]
D(x) = 1/2 eta ||Proj_[xmin;xmax]-x||^2
-> a quadratic elastic net term allowing to ensure the existence of the solution 
E(x) = tau ||x||^2
-> a regularization term favorizing piecewise constant images
R(x) = lambda sum(phi(V(x)))
where V is a linear operator computing the first-order differences between pixels
(i.e. the discrete gradient computed in the horizontal and
vertical directions) and phi is one of the following potential functions
%(1) phi(u) = (1-exp(-u.^2./(2*delta^2)));  %NON CONVEX - NON COERCIVE
%(2) phi(u) = (u.^2)./(2*delta^2 + u.^2);   %NON CONVEX - NON COERCIVE
%(3) phi(u) = log(1 + (u.^2)./(delta^2));   %NON CONVEX - COERCIVE
%(4) phi(u) = sqrt(1 + u^2/delta^2)-1;      %CONVEX 
%(5) phi(u) = 1/2 u^2;                      %CONVEX
 
The restoration process uses the Majorize-Minimize Memory Gradient Algorithm. 

This toolbox consists of 2 subfolders:
1) Images  : contains some standard test images
2) Include : contains the restoration program.


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SPECIFICATIONS for using RestoMMMG:

Two demo files are provided :
* demodenoising.m runs a restoration example. 
* demodeblurring.m runs a deconvolution example. 


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RELATED PUBLICATIONS:

# E. Chouzenoux, J. Idier and S. Moussaoui. "A Majorize-Minimize Strategy
 for Subspace Optimization Applied to Image Restoration" 
 IEEE Transactions on Image Processing, Vol. 20, No. 18, pages 1517-1528, juin 2011
  

# E. Chouzenoux, J.-C. Pesquet, H. Talbot and A. Jezierska. "A Memory
 Gradient Algorithm for l2-l0 Regularization with Applications to Image Restoration. "
 In Proc. IEEE ICIP 2011.
 
# E. Chouzenoux. Recherche de pas par Majoration-Minoration. Application � la r�solution de probl�mes inverses.
Th�se de doctorat, Ecole Centrale de Nantes, d�cembre 2010
http://tel.archives-ouvertes.fr/tel-00555643/fr/

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