English

A signal recovery algorithm for sparse matrix based compressed sensing

Information Theory 2011-02-21 v1 Disordered Systems and Neural Networks math.IT

Abstract

We have developed an approximate signal recovery algorithm with low computational cost for compressed sensing on the basis of randomly constructed sparse measurement matrices. The law of large numbers and the central limit theorem suggest that the developed algorithm saturates the Donoho-Tanner weak threshold for the perfect recovery when the matrix becomes as dense as the signal size NN and the number of measurements MM tends to infinity keep α=M/NO(1)\alpha=M/N \sim O(1), which is supported by extensive numerical experiments. Even when the numbers of non-zero entries per column/row in the measurement matrices are limited to O(1)O(1), numerical experiments indicate that the algorithm can still typically recover the original signal perfectly with an O(N)O(N) computational cost per update as well if the density ρ\rho of non-zero entries of the signal is lower than a certain critical value ρth(α)\rho_{\rm th}(\alpha) as N,MN,M \to \infty.

Keywords

Cite

@article{arxiv.1102.3220,
  title  = {A signal recovery algorithm for sparse matrix based compressed sensing},
  author = {Yoshiyuki Kabashima and Tadashi Wadayama},
  journal= {arXiv preprint arXiv:1102.3220},
  year   = {2011}
}

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Submitted to ISIT2011

R2 v1 2026-06-21T17:26:58.637Z