Stability of low-rank matrix recovery and its connections to Banach space geometry

Javier Alejandro Chávez-Domínguez, Denka Kutzarova

Research output: Contribution to journalArticlepeer-review

Abstract

There are well-known relationships between compressed sensing and the geometry of the finite-dimensional ℓp spaces. A result of Kashin and Temlyakov [20] can be described as a characterization of the stability of the recovery of sparse vectors via ℓ1-minimization in terms of the Gelfand widths of certain identity mappings between finite-dimensional ℓ1 and ℓ2 spaces, whereas a more recent result of Foucart, Pajor, Rauhut and Ullrich [16] proves an analogous relationship even for ℓp spaces with p<1. In this paper we prove what we call matrix or noncommutative versions of these results: we characterize the stability of low-rank matrix recovery via Schatten p-(quasi-)norm minimization in terms of the Gelfand widths of certain identity mappings between finite-dimensional Schatten p-spaces.

Original languageEnglish (US)
Pages (from-to)320-335
Number of pages16
JournalJournal of Mathematical Analysis and Applications
Volume427
Issue number1
DOIs
StatePublished - Jul 1 2015

Keywords

  • Compressed sensing
  • Gelfand widths
  • Low-rank matrix recovery
  • Schatten p-minimization

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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