A priori on the hyperparameters 

To obtain the unicity of the optimal couple 
We could estimate not only but also . Currently must be fixed, because of the existence of an infinity of local maxima of the likelihood (one for each ).
 

For a best quality image reconstruction

Towards a more local approach : adaptive  and  parameters

  Too global approach with only one couple  for a large size image.

 Results depend on the choice of an estimation area : see example.