Unbiased Risk Estimation for Sparse Analysis Regularization
Language
en
Communication dans un congrès
This item was published in
Proc. ICIP'12, Proc. ICIP'12, Proc. ICIP'12, 2012-09, Orlando. 2012-09p. 3053-3056
English Abstract
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 ...Read more >
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.Read less <
English Keywords
Sparsity
analysis regularization
inverse problems
risk estimator
GSURE
European Project
SIGMA-Vision
ANR Project
Adaptivité pour la représentation des images naturelles et des textures - ANR-08-EMER-0009
Origin
Hal imported