Sure independence screening and compressed random sensing

Lingzhou Xue, Hui Zou

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

Compressed sensing is a very powerful and popular tool for sparse recovery of high dimensional signals. Random sensing matrices are often employed in compressed sensing. In this paper we introduce a new method named aggressive betting using sure independence screening for sparse noiseless signal recovery. The proposal exploits the randomness structure of random sensing matrices to greatly boost computation speed. When using sub-Gaussian sensing matrices, which include the Gaussian and Bernoulli sensing matrices as special cases, our proposal has the exact recovery property with overwhelming probability. We also consider sparse recovery with noise and explicitly reveal the impact of noise-to-signal ratio on the probability of sure screening.

Original languageEnglish (US)
Pages (from-to)371-380
Number of pages10
JournalBiometrika
Volume98
Issue number2
DOIs
StatePublished - Jun 1 2011

Fingerprint

Screening
Sensing
Recovery
screening
Compressed sensing
Compressed Sensing
Signal-To-Noise Ratio
Noise
Bernoulli
Randomness
Signal to noise ratio
High-dimensional
Independence
methodology

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

Cite this

Xue, Lingzhou ; Zou, Hui. / Sure independence screening and compressed random sensing. In: Biometrika. 2011 ; Vol. 98, No. 2. pp. 371-380.
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Sure independence screening and compressed random sensing. / Xue, Lingzhou; Zou, Hui.

In: Biometrika, Vol. 98, No. 2, 01.06.2011, p. 371-380.

Research output: Contribution to journalArticle

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