English

Compressive sensing by white random convolution

Optimization and Control 2009-09-30 v2 Information Theory math.IT

Abstract

A different compressive sensing framework, convolution with white noise waveform followed by subsampling at fixed (not randomly selected) locations, is studied in this paper. We show that its recoverability for sparse signals depends on the coherence (denoted by mu) between the signal representation and the Fourier basis. In particular, an n-dimensional signal which is S-sparse in such a basis can be recovered with a probability exceeding 1-delta from any fixed m~O(mu^2*S*log(n/delta)^(3/2)) output samples of the random convolution.

Keywords

Cite

@article{arxiv.0909.2737,
  title  = {Compressive sensing by white random convolution},
  author = {Yin Xiang and Lianlin Li and Fang Li},
  journal= {arXiv preprint arXiv:0909.2737},
  year   = {2009}
}

Comments

10 pages with 4 figures

R2 v1 2026-06-21T13:46:32.738Z