Sparse Signal Recovery with Multiple Prior Information: Algorithm and Measurement Bounds

Huynh Van Luong*, Nikos Deligiannis, Jürgen Seiler, Søren Forchhammer, André Kaup

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

We address the problem of reconstructing a sparse signal from compressive measurements with the aid of multiple known correlated signals. We propose a reconstruction algorithm with multiple side information signals (RAMSI), which solves an minimization problem by weighting adaptively the multiple side information signals at every iteration. In addition, we establish theoretical bounds on the number of measurements required to guarantee successful reconstruction of the sparse signal via weighted minimization. The analysis of the derived bounds reveals that weighted minimization can achieve sharper bounds and significant performance improvements compared to classical compressed sensing (CS). We evaluate experimentally the proposed RAMSI algorithm and the established bounds using numerical sparse signals. The results show that the proposed algorithm outperforms state-of-the-art algorithms—including classical CS, ℓ1-ℓ1 minimization, Modified-CS, regularized Modified-CS, and weighted ℓ1 minimization—in terms of both the theoretical bounds and the practical performance.
Original languageEnglish
JournalSignal Processing
Volume152
Pages (from-to)417-428
ISSN0165-1684
DOIs
Publication statusPublished - 2018

Keywords

  • Compressed sensing
  • Prior information
  • Weighted n-`1
  • Minimization
  • Measurement bounds

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