Stein COnsistent Risk Estimator (SCORE) for hard thresholding

Deledalle, Charles-Alban; Peyré, Gabriel; Fadili, Jalal M.

Deledalle, Charles-Alban; Peyré, Gabriel; Fadili, Jalal M. (2013), Stein COnsistent Risk Estimator (SCORE) for hard thresholding, Signal Processing with Adaptive Sparse Structured Representations, 2013-07, Lausanne, Switzerland

Type

Communication / Conférence

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https://hal.archives-ouvertes.fr/hal-00776303

Date

2013

Titre du colloque

Signal Processing with Adaptive Sparse Structured Representations

Date du colloque

2013-07

Ville du colloque

Lausanne

Pays du colloque

Switzerland

Métadonnées

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Auteur(s)

Deledalle, Charles-Alban
Institut de Mathématiques de Bordeaux [IMB]
Peyré, Gabriel
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Fadili, Jalal M.
Groupe de Recherche en Informatique, Image et Instrumentation de Caen [GREYC]

Résumé (EN)

In this work, we construct a risk estimator for hard thresholding which can be used as a basis to solve the difficult task of automatically selecting the threshold. As hard thresholding is not even continuous, Stein's lemma cannot be used to get an unbiased estimator of degrees of freedom, hence of the risk. We prove that under a mild condition, our estimator of the degrees of freedom, although biased, is consistent. Numerical evidence shows that our estimator outperforms another biased risk estimator.

Mots-clés

risk estimation; hard thresholding; sparsity; threshold selection