PANDORE Version 6
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mca



Morphological Component Analysis of a 2D images (a matrix) using highly redundant dictionaries. MCA is very useful for separating sources based on their morphological diversity.



Synopsis

mca itermax cartoon gamma expdecrease stop [dict_in|-] [im_in|-] [im_out|-]

Description

The MCA solves the ollowing optimization problem using a modified version of the BCR algorithm:
  (part_a,part_b) = argmin0.5 ||img - Sum_i part_i||_2^2 +  lambda * Sum_i || \Phi^T_i part_i ||_p + gamma * TV(cartoon part)
   p = 1 (l_1 norm: Soft thesholding as a solution).
   p = 0 (l_0 norm: difficult but approximated with a Hard thresholding).
 Each component part_i is supposed to be sparsely described in its corresponding dictionary \Phi.

Parameters

itermax          
Nb of relaxation iterations
cartoon        
Index of the part considered as the cartoon. This index must match one of the transforms (parts) in the dictionary. TV constraint is not allowed on some transforms, e.g. corresponding to warped oscillatory patterns.
gamma          
TV regularization parameter (usually applied to the cartoon smooth component, e.g. sparsely represented by a wavelet or curvelet dictionary.
expdecrease   
Exponential/Linear decrease of the regularization parameter.
stop               
Stop criterion, the algorithm stops when lambda <= stop*sigma (typically k=3), sigma is the noise WGN std.

Inputs

  • dict_in : input overcomplete dictionary (see dictionary).
  • im_in   : 2D image matrix, nxn, n = 2^J.

Outputs

  • im_out : Estimated semantic components (nb components x n x n image).

Result

Retruns SUCCESS or FAILURE.

See also

dictionary, eminpaint

Prototype C++

Errc MCA(Img2dsf & ims, Dictionary& dict, Ulong itermax, int cartoon_part, Float gamma, int expdecrease, Float stop, Img3dsf & imd)


Authors: Jalal Fadili, Remy Yannick, Ouedraogo Nael