Adaptive Structured Block Sparsity Via Dyadic Partitioning

Chesneau, Christophe; Fadili, Jalal; Peyré, Gabriel

Chesneau, Christophe; Fadili, Jalal; Peyré, Gabriel (2011), Adaptive Structured Block Sparsity Via Dyadic Partitioning, EUSIPCO 2011, 2011-08, Barcelone, Espagne

Type

Communication / Conférence

External document link

http://hal.archives-ouvertes.fr/hal-00597772/fr/

Date

2011

Conference title

EUSIPCO 2011

Conference date

2011-08

Conference city

Barcelone

Conference country

Espagne

Metadata

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Author(s)

Chesneau, Christophe
Fadili, Jalal
Peyré, Gabriel

Abstract (EN)

This paper proposes a novel method to adapt the block-sparsity structure to the observed noisy data. Towards this goal, the Stein risk estimator framework is exploited, and the block-sparsity is dyadically organized in a tree. The adaptation of the sparsity structure is obtained by finding the best recursive dyadic partition, whose terminal nodes (leaves) are the blocks, that minimizes a data-driven estimator of the risk. Our main contributions are (i) analytical expression of the risk; (ii) a novel estimator of the risk; (iii) a fast algorithm that yields the best partition. Numerical results on wavelet-domain denoising of synthetic and natural images illustrate the improvement brought by our adaptive approach.

Subjects / Keywords

dyadic partition; Stein risk; block-sparsity