with 
.
The regularization by the significant structures leads to:
The basic idea of our method consists of detecting, at each scale,
structures of a given size in the residual 
and putting
them in the restored image 
. The process finishes when
no more structures are detected. Then, we have separated the image
into two images 
and 
. 
is
the restored image, which does not contain any noise, and 
is
the final residual which does not contain any structure. R is our
estimation of the noise 
.