Recovery of Structured Signals With Prior Information via Maximizing Correlation

Xu Zhang, Wei Cui, Yulong Liu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

This paper considers the problem of recovering a structured signal from a relatively small number of noisy measurements with the aid of a similar signal which is known beforehand. We propose a new approach to integrate prior information into the standard recovery procedure by maximizing the correlation between the prior knowledge and the desired signal. We then establish performance guarantees (in terms of the number of measurements) for the proposed method under sub-Gaussian measurements. Specific structured signals including sparse vectors, block-sparse vectors, and low-rank matrices are also analyzed. Furthermore, we present an interesting geometrical interpretation for the proposed procedure. Our results demonstrate that if prior information is good enough, then the proposed approach can (remarkably) outperform the standard recovery procedure. Simulations are provided to verify our results.

Original languageEnglish
Pages (from-to)3296-3310
Number of pages15
JournalIEEE Transactions on Signal Processing
Volume66
Issue number12
DOIs
Publication statusPublished - 15 Jun 2018

Keywords

  • Compressed sensing
  • Gaussian width
  • maximizing correlation
  • prior information
  • structured signals

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