For optimal restoration of space invariant and variant degradation many researchers have proposed ANNs and Steepest Descent approaches for decades. Please share if you have found any good surveys on them.
you might take a look at sparse coding and dictionary learning techniques
J. Mairal, F. Bach, J. Ponce, G. Sapiro and A. Zisserman. Non-Local Sparse Models for Image Restoration. International Conference on Computer Vision (ICCV), 2009
available here
http://www.di.ens.fr/~fbach/
with a lot of material related to sparse coding
The SPArse Modelling Software (SPAMS) can be downloaded here
"It includes fast implementations of LARS, OMP, a dictionary learning algorithm and its variants for NMF, sparse PCA, as well as efficient sparse solvers based on proximal methods. "