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

External document link

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

Date

2013

Conference title

Signal Processing with Adaptive Sparse Structured Representations

Conference date

2013-07

Conference city

Lausanne

Conference country

Switzerland

Metadata

Show full item record

Author(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]

Abstract (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.

Subjects / Keywords

risk estimation; hard thresholding; sparsity; threshold selection