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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

Type
Communication / Conférence
External document link
http://hal.archives-ouvertes.fr/hal-00662718
Date
2012
Conference title
2012 IEEE International Conference on Image Processing (ICIP)
Conference date
2012-10
Conference city
Orlando
Conference country
Etats-Unis
Book title
19th IEEE International Conference on Image Processing (ICIP), 2012 - proceedings
Publisher
IEEE
ISBN
978-1-4673-2534-9
Pages
3053-3056
Publication identifier
http://dx.doi.org/10.1109/ICIP.2012.6467544
Metadata
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Author(s)
Dossal, Charles
Fadili, Jalal
Peyré, Gabriel
Vaiter, Samuel cc
Deledalle, Charles-Alban
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 / Keywords
GSURE; risk estimator; inverse problems; analysis regularization; Sparsity

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