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Mathematics > Optimization and Control

arXiv:0909.2737 (math)
[Submitted on 15 Sep 2009 (v1), last revised 30 Sep 2009 (this version, v2)]

Title:Compressive sensing by white random convolution

Authors:Yin Xiang, Lianlin Li, Fang Li
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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.
Comments: 10 pages with 4 figures
Subjects: Optimization and Control (math.OC); Information Theory (cs.IT)
MSC classes: 68P30
Cite as: arXiv:0909.2737 [math.OC]
  (or arXiv:0909.2737v2 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.0909.2737

Submission history

From: Yin Xiang [view email]
[v1] Tue, 15 Sep 2009 08:05:42 UTC (337 KB)
[v2] Wed, 30 Sep 2009 09:32:15 UTC (298 KB)
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