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The different probability laws :
- Y follows a Gaussian distribution N (), N=Y-HX :
- The prior is given by a Gibbsian probability, because X is supposed to be a Markov random field.
likelihood can be rewritten in the form :
Z, ZY = partition functions (cf. statistical mechanics) ,
they are normalizing constants.
is the set of images with M grey levels.
, at least :
Impossible to directly calculate the partition functions !
because of the dimension of the space.
We do not try to calculate them, but to estimate them.