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The MCMCML estimation algorithm
 
"Markov Chain Monte Carlo Maximum Likelihood"
 

Minimization of the -log likelihood :
 

  
 
Descent method : we use the gradient of the criterion w.r.t.  and .

  is fixed and we only compute , the gradient of the criterion w.r.t. .
  is fixed because for each  we can find a value of  for which  is optimal.
Estimation and restoration processes are simultaneous :
       (the modified Geman-Yang sampler is initialized with )
 
 

The MCMCML estimation algorithm
Initialization : 
-  chosen in order to penalize the gradients due to noise 
   and to preserve edges.  
- The ratio  corresponds to the best Wiener filter. 
Compute: 
is reconstructed from Y with the ICM-DCT algorithm,  
with the current couple .
Compute  and  : 
Generate 2 Markov chains with the Modified Geman-Yang algorithm : 

  sampled from the prior model  
       etc. 

  sampled from the posterior distribution 
       etc. 

Compute the empirical mean :  

Iteration from  to  : 
where  (to  ensure convergence)
 
Stop criterion : 
We stop the algorithm if  
where  is the estimation error (%) fixed at the beginning. 
 
 
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André Jalobeanu - 24 Aug 1998