Compressive sensing by white random convolution

Details Compressive sensing by white random convolution Compressive sensing by white random convolution

2009-09-15

arxiv.org/abs/0909.2737v2

Mathematics

Optimization and Control

10 pages with 4 figures

Scientific paper

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.

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