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.

The likelihood can be rewritten in the form :
 

Z, Z_Y = 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.