Strengthening hash families and compressive sensing

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

The deterministic construction of measurement matrices for compressive sensing is a challenging problem, for which a number of combinatorial techniques have been developed. One of them employs a widely used column replacement technique based on hash families. It is effective at producing larger measurement matrices from smaller ones, but it can only preserve the strength (level of sparsity supported), not increase it. Column replacement is extended here to produce measurement matrices with larger strength from ingredient arrays with smaller strength. To do this, a new type of hash family, called a strengthening hash family, is introduced. Using these hash families, column replacement is shown to increase strength under two standard notions of recoverability. Then techniques to construct strengthening hash families, both probabilistically and deterministically, are developed. Using a variant of the Stein-Lovász-Johnson theorem, a deterministic, polynomial time algorithm for constructing a strengthening hash family of fixed strength is derived.

Original languageEnglish (US)
Pages (from-to)170-186
Number of pages17
JournalJournal of Discrete Algorithms
Volume16
DOIs
StatePublished - Oct 2012

Keywords

  • Column replacement
  • Compressive sensing
  • Hash family
  • Lovász local lemma
  • Stein-Lovász- Johnson theorem

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

Fingerprint Dive into the research topics of 'Strengthening hash families and compressive sensing'. Together they form a unique fingerprint.

Cite this