We have to optimize a criterion which depends on the hyperparameters.  It is the Maximum Likelihood Estimator on the observed image Y w.r.t.  and :

   maximizing a probability w.r.t. and :
 

where  = set of images , with M grey levels

 

	probability to obtain the data Y from the initial image X, (joint likelihood of X and hyperparameters)
	a priori probability on the image X  calculated only taking into account the constraints characterizes the type of regularization  -function