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.
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