Proximal Splitting Derivatives for Risk Estimation
Deledalle, Charles-Alban; Vaiter, Samuel; Peyré, Gabriel; Fadili, Jalal; Dossal, Charles (2012), Proximal Splitting Derivatives for Risk Estimation, 2nd International Workshop on New Computational Methods for Inverse Problems (NCMIP 2012), 2012-05, Cachan, France
TypeCommunication / Conférence
External document linkhttp://hal.archives-ouvertes.fr/hal-00670213
Conference title2nd International Workshop on New Computational Methods for Inverse Problems (NCMIP 2012)
Journal nameJournal of Physics: Conference Series
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Abstract (EN)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.
Subjects / KeywordsSparsity; regularization; inverse problems; risk estimator; GSURE; automatic differentiation
Showing items related by title and author.
Fadili, Jalal; Dossal, Charles; Peyré, Gabriel; Deledalle, Charles-Alban; Vaiter, Samuel (2013) Article accepté pour publication ou publié
Fadili, Jalal; Peyré, Gabriel; Vaiter, Samuel; Deledalle, Charles-Alban (2014) Article accepté pour publication ou publié