Identification of sparse linear operators

Reinhard Heckel, Helmut Bolcskei

Research output: Contribution to journalArticlepeer-review

29 Scopus citations

Abstract

We consider the problem of identifying a linear deterministic operator from its response to a given probing signal. For a large class of linear operators, we show that stable identifiability is possible if the total support area of the operator's spreading function satisfies δ ≤ 1/2. This result holds for an arbitrary (possibly fragmented) support region of the spreading function, does not impose limitations on the total extent of the support region, and, most importantly, does not require the support region to be known prior to identification. Furthermore, we prove that stable identifiability of almost all operators is possible if δ < 1. This result is surprising as it says that there is no penalty for not knowing the support region of the spreading function prior to identification. Algorithms that provably recover all operators with δ ≤1/2, and almost all operators with δ < 1 are presented.

Original languageEnglish
Article number6630107
Pages (from-to)7985-8000
Number of pages16
JournalIEEE Transactions on Information Theory
Volume59
Issue number12
DOIs
StatePublished - Dec 2013
Externally publishedYes

Keywords

  • Compressed sensing
  • sparsity
  • system identification

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