HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information

# Unbiased Risk Estimation for Sparse Analysis Regularization

2 Equipe Image - Laboratoire GREYC - UMR6072
GREYC - Groupe de Recherche en Informatique, Image et Instrumentation de Caen
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 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.
Keywords :
Document type :
Conference papers
Domain :
Complete list of metadata

Cited literature [17 references]

https://hal.archives-ouvertes.fr/hal-00662718
Contributor : Gabriel Peyré Connect in order to contact the contributor
Submitted on : Tuesday, January 24, 2012 - 10:09:28 PM
Last modification on : Tuesday, January 18, 2022 - 3:24:30 PM
Long-term archiving on: : Monday, November 19, 2012 - 2:35:08 PM

### File

sure-analysis-icip2012.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : hal-00662718, version 1

### Citation

Charles Deledalle, Samuel Vaiter, Gabriel Peyré, Jalal M. Fadili, Charles Dossal. Unbiased Risk Estimation for Sparse Analysis Regularization. Proc. ICIP'12, Sep 2012, Orlando, United States. pp.3053-3056. ⟨hal-00662718⟩

Record views