On the support of compressed modes

Farzin Barekat; Russel Caflisch; Stanley Osher

doi:10.1137/140956725

On the support of compressed modes

Farzin Barekat, Russel Caflisch, Stanley Osher

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Compressed modes are solutions of the Laplace equation with a potential and a subgradient term. The subgradient term comes from addition of an L¹ penalty in the corresponding variational principle. This paper presents an analysis of compressed modes, finding the minimizer of the variational principle, showing the spatial localization property of compressed modes, and establishing an upper bound on the volume of their support.

Original language	English (US)
Pages (from-to)	2573-2590
Number of pages	18
Journal	SIAM Journal on Mathematical Analysis
Volume	49
Issue number	4
DOIs	https://doi.org/10.1137/140956725
State	Published - 2017

Keywords

Compressed modes
Compressive sensing
L-regularization
PDE
Sparsity

ASJC Scopus subject areas

Analysis
Computational Mathematics
Applied Mathematics

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10.1137/140956725

Cite this

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abstract = "Compressed modes are solutions of the Laplace equation with a potential and a subgradient term. The subgradient term comes from addition of an L1 penalty in the corresponding variational principle. This paper presents an analysis of compressed modes, finding the minimizer of the variational principle, showing the spatial localization property of compressed modes, and establishing an upper bound on the volume of their support.",

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AB - Compressed modes are solutions of the Laplace equation with a potential and a subgradient term. The subgradient term comes from addition of an L1 penalty in the corresponding variational principle. This paper presents an analysis of compressed modes, finding the minimizer of the variational principle, showing the spatial localization property of compressed modes, and establishing an upper bound on the volume of their support.

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KW - L-regularization

KW - PDE

KW - Sparsity

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On the support of compressed modes

Abstract

Keywords

ASJC Scopus subject areas

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