Unbiased Risk Estimation for Sparse Analysis Regularization
Dossal, Charles; Fadili, Jalal; Peyré, Gabriel; Vaiter, Samuel; Deledalle, Charles-Alban (2012), Unbiased Risk Estimation for Sparse Analysis Regularization, 19th IEEE International Conference on Image Processing (ICIP), 2012 - proceedings, IEEE, p. 3053-3056
TypeCommunication / Conférence
External document linkhttp://hal.archives-ouvertes.fr/hal-00662718
Conference title2012 IEEE International Conference on Image Processing (ICIP)
Book title19th IEEE International Conference on Image Processing (ICIP), 2012 - proceedings
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Abstract (EN)In this paper, we propose a rigorous derivation of the expression of the projected Generalized Stein Unbiased Risk Estimator ($\GSURE$) for the estimation of the (projected) risk associated to regularized ill-posed linear inverse problems using sparsity-promoting L1 penalty. The projected GSURE is an unbiased estimator of the recovery risk on the vector projected on the orthogonal of the degradation operator kernel. Our framework can handle many well-known regularizations including sparse synthesis- (e.g. wavelet) and analysis-type priors (e.g. total variation). A distinctive novelty of this work is that, unlike previously proposed L1 risk estimators, we have a closed-form expression that can be implemented efficiently once the solution of the inverse problem is computed. To support our claims, numerical examples on ill-posed inverse problems with analysis and synthesis regularizations are reported where our GSURE estimates are used to tune the regularization parameter.
Subjects / KeywordsGSURE; risk estimator; inverse problems; analysis regularization; Sparsity
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