On the support of compressed modes

Farzin Barekat, Russel Caflisch, Stanley Osher

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)2573-2590
Number of pages18
JournalSIAM Journal on Mathematical Analysis
Volume49
Issue number4
DOIs
StatePublished - 2017

Fingerprint

Laplace equation
Subgradient
Variational Principle
Term
Laplace's equation
Minimizer
Penalty
Upper bound

Keywords

  • Compressed modes
  • Compressive sensing
  • L-regularization
  • PDE
  • Sparsity

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

Cite this

On the support of compressed modes. / Barekat, Farzin; Caflisch, Russel; Osher, Stanley.

In: SIAM Journal on Mathematical Analysis, Vol. 49, No. 4, 2017, p. 2573-2590.

Research output: Contribution to journalArticle

Barekat, F, Caflisch, R & Osher, S 2017, 'On the support of compressed modes', SIAM Journal on Mathematical Analysis, vol. 49, no. 4, pp. 2573-2590. https://doi.org/10.1137/140956725
Barekat, Farzin ; Caflisch, Russel ; Osher, Stanley. / On the support of compressed modes. In: SIAM Journal on Mathematical Analysis. 2017 ; Vol. 49, No. 4. pp. 2573-2590.
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