Name
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. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1109/ICIP.2012.6467544 | Image Processing |
Keywords | Field | DocType |
image processing,inverse problems,risk analysis,sparse matrices,vectors,wavelet transforms,analysis-type priors,closed-form expression,degradation operator kernel orthogonal,projected GSURE,projected generalized Stein unbiased risk estimator expression,recovery risk unbiased estimator,regularization parameter analysis,regularization parameter synthesis,regularized ill-posed linear inverse problems,sparse analysis regularization,sparse synthesis,sparsity-promoting ℓ1penalty,total variation,vector projection,wavelet synthesis,GSURE,Sparsity,analysis regularization,inverse problems,risk estimator | Applied mathematics,Computer science,Bias of an estimator,Regularization (mathematics),Inverse problem,Artificial intelligence,Sparse matrix,Kernel (linear algebra),Mathematical optimization,Stein's unbiased risk estimate,Pattern recognition,Prior probability,Estimator | Conference |
ISSN | ISBN | Citations |
1522-4880 E-ISBN : 978-1-4673-2532-5 | 978-1-4673-2532-5 | 4 |
PageRank | References | Authors |
0.51 | 6 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Charles-Alban Deledalle | 1 | 418 | 15.24 |
| Vaiter, S. | 2 | 4 | 0.51 |
| Gabriel Peyré | 3 | 1195 | 79.60 |
| Jalal Fadili | 4 | 1184 | 80.08 |