Proximal Splitting Derivatives for Risk Estimation
Language
en
Communication dans un congrès
This item was published in
Journal of Physics: Conference Series, Proc. 2nd Int. Workshop on New Computational Methods for Inverse Problems (NCMIP 2012), Proc. 2nd Int. Workshop on New Computational Methods for Inverse Problems (NCMIP 2012), NCMIP'12, 2012-04. 2012-04, vol. 386, p. 012003
IOP Science
English Abstract
This paper develops a novel framework to compute a projected Generalized Stein Unbiased Risk Estimator (GSURE) for a wide class of sparsely regularized solutions of inverse problems. This class includes arbitrary convex ...Read more >
This paper develops a novel framework to compute a projected Generalized Stein Unbiased Risk Estimator (GSURE) for a wide class of sparsely regularized solutions of inverse problems. This class includes arbitrary convex data fidelities with both analysis and synthesis mixed L1-L2 norms. The GSURE necessitates to compute the (weak) derivative of a solution w.r.t.~the observations. However, as the solution is not available in analytical form but rather through iterative schemes such as proximal splitting, we propose to iteratively compute the GSURE by differentiating the sequence of iterates. This provides us with a sequence of differential mappings, which, hopefully, converge to the desired derivative and allows to compute the GSURE. We illustrate this approach on total variation regularization with Gaussian noise and to sparse regularization with poisson noise, to automatically select the regularization parameter.Read less <
Italian Keywords
Sparsity
regularization
inverse problems
risk estimator
GSURE
automatic differentiation
European Project
ERC SIGMA-Vision
ANR Project
Adaptivité pour la représentation des images naturelles et des textures - ANR-08-EMER-0009
Origin
Hal imported