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Chirp sensing codes: Deterministic compressed sensing measurements for fast recovery

Publication ,  Journal Article
Applebaum, L; Howard, SD; Searle, S; Calderbank, R
Published in: Applied and Computational Harmonic Analysis
March 1, 2009

Compressed sensing is a novel technique to acquire sparse signals with few measurements. Normally, compressed sensing uses random projections as measurements. Here we design deterministic measurements and an algorithm to accomplish signal recovery with computational efficiency. A measurement matrix is designed with chirp sequences forming the columns. Chirps are used since an efficient method using FFTs can recover the parameters of a small superposition. We show that this type of matrix is valid as compressed sensing measurements. This is done by bounding the eigenvalues of sub-matrices, as well as an empirical comparison with random projections. Further, by implementing our algorithm, simulations show successful recovery of signals with sparsity levels similar to those possible by matching pursuit with random measurements. For sufficiently sparse signals, our algorithm recovers the signal with computational complexity O (K log K) for K measurements. This is a significant improvement over existing algorithms. Crown Copyright © 2008.

Duke Scholars

Published In

Applied and Computational Harmonic Analysis

DOI

EISSN

1096-603X

ISSN

1063-5203

Publication Date

March 1, 2009

Volume

26

Issue

2

Start / End Page

283 / 290

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics
 

Citation

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Applebaum, L., Howard, S. D., Searle, S., & Calderbank, R. (2009). Chirp sensing codes: Deterministic compressed sensing measurements for fast recovery. Applied and Computational Harmonic Analysis, 26(2), 283–290. https://doi.org/10.1016/j.acha.2008.08.002
Applebaum, L., S. D. Howard, S. Searle, and R. Calderbank. “Chirp sensing codes: Deterministic compressed sensing measurements for fast recovery.” Applied and Computational Harmonic Analysis 26, no. 2 (March 1, 2009): 283–90. https://doi.org/10.1016/j.acha.2008.08.002.
Applebaum L, Howard SD, Searle S, Calderbank R. Chirp sensing codes: Deterministic compressed sensing measurements for fast recovery. Applied and Computational Harmonic Analysis. 2009 Mar 1;26(2):283–90.
Applebaum, L., et al. “Chirp sensing codes: Deterministic compressed sensing measurements for fast recovery.” Applied and Computational Harmonic Analysis, vol. 26, no. 2, Mar. 2009, pp. 283–90. Scopus, doi:10.1016/j.acha.2008.08.002.
Applebaum L, Howard SD, Searle S, Calderbank R. Chirp sensing codes: Deterministic compressed sensing measurements for fast recovery. Applied and Computational Harmonic Analysis. 2009 Mar 1;26(2):283–290.
Journal cover image

Published In

Applied and Computational Harmonic Analysis

DOI

EISSN

1096-603X

ISSN

1063-5203

Publication Date

March 1, 2009

Volume

26

Issue

2

Start / End Page

283 / 290

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics