On the support of compressed modes

Farzin Barekat, Russel Caflisch, Stanley Osher

Research output: Contribution to journalArticlepeer-review


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
Issue number4
StatePublished - 2017


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

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics


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