Previous Contents Next
Previous: The modified Geman-Yang...  Next : The reconstruction algorithm 
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. 
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  

  sampled from the posterior distribution 

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. 
Previous Next
André Jalobeanu - 24 Aug 1998