Derandomizing Restricted Isometries via the Legendre Symbol

Afonso Bandeira, Matthew Fickus, Dustin G. Mixon, Joel Moreira

Research output: Contribution to journalArticle

Abstract

The restricted isometry property (RIP) is an important matrix condition in compressed sensing, but the best matrix constructions to date use randomness. This paper leverages pseudorandom properties of the Legendre symbol to reduce the number of random bits in an RIP matrix with Bernoulli entries. In this regard, the Legendre symbol is not special—our main result naturally generalizes to any small-bias sample space. We also conjecture that no random bits are necessary for our Legendre symbol-based construction.

Original languageEnglish (US)
Pages (from-to)409-424
Number of pages16
JournalConstructive Approximation
Volume43
Issue number3
DOIs
StatePublished - Jun 1 2016

Fingerprint

Legendre
Isometry
Compressed sensing
Sample space
Compressed Sensing
Bernoulli
Leverage
Randomness
Generalise
Necessary

Keywords

  • Compressed sensing
  • Derandomization
  • Legendre symbol
  • Restricted isometry property
  • Small-bias sample space

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)
  • Computational Mathematics

Cite this

Derandomizing Restricted Isometries via the Legendre Symbol. / Bandeira, Afonso; Fickus, Matthew; Mixon, Dustin G.; Moreira, Joel.

In: Constructive Approximation, Vol. 43, No. 3, 01.06.2016, p. 409-424.

Research output: Contribution to journalArticle

Bandeira, A, Fickus, M, Mixon, DG & Moreira, J 2016, 'Derandomizing Restricted Isometries via the Legendre Symbol', Constructive Approximation, vol. 43, no. 3, pp. 409-424. https://doi.org/10.1007/s00365-015-9310-6
Bandeira, Afonso ; Fickus, Matthew ; Mixon, Dustin G. ; Moreira, Joel. / Derandomizing Restricted Isometries via the Legendre Symbol. In: Constructive Approximation. 2016 ; Vol. 43, No. 3. pp. 409-424.
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