Chirp sensing codes: Deterministic compressed sensing measurements for fast recovery

Journal Article (Letter;Journal)

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.

Full Text

Duke Authors

Cited Authors

  • Applebaum, L; Howard, SD; Searle, S; Calderbank, R

Published Date

  • March 1, 2009

Published In

Volume / Issue

  • 26 / 2

Start / End Page

  • 283 - 290

Electronic International Standard Serial Number (EISSN)

  • 1096-603X

International Standard Serial Number (ISSN)

  • 1063-5203

Digital Object Identifier (DOI)

  • 10.1016/j.acha.2008.08.002

Citation Source

  • Scopus