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preprint · arXiv (Cornell University) · 2010

"Compressed" Compressed Sensing

Galen Reeves, Michael Gastpar

Cited by 0Open access

Abstract

The field of compressed sensing has shown that a sparse but otherwise arbitrary vector can be recovered exactly from a small number of randomly constructed linear projections (or samples). The question addressed in this paper is whether an even smaller number of samples is sufficient when there exists prior knowledge about the distribution of the unknown vector, or when only partial recovery is needed. An information-theoretic lower bound with connections to free probability theory and an upper bound corresponding to a computationally simple thresholding estimator are derived. It is shown that in certain cases (e.g. discrete valued vectors or large distortions) the number of samples can be decreased. Interestingly though, it is also shown that in many cases no reduction is possible.

Cite this paper

APA 7

Reeves, G., & Gastpar, M. (2010). "Compressed" Compressed Sensing. arXiv (Cornell University). https://doi.org/10.48550/arxiv.1001.4295

MLA 9

Reeves, Galen, and Michael Gastpar. “"Compressed" Compressed Sensing.” arXiv (Cornell University), 2010, https://doi.org/10.48550/arxiv.1001.4295.

Chicago

Reeves, Galen, and Michael Gastpar. 2010. “"Compressed" Compressed Sensing.” arXiv (Cornell University). https://doi.org/10.48550/arxiv.1001.4295.

Harvard

Reeves, G. and Gastpar, M. (2010) ‘"Compressed" Compressed Sensing’, arXiv (Cornell University). Available at: https://doi.org/10.48550/arxiv.1001.4295.

BibTeX
@misc{reeves2010compressed,
  title = {{"Compressed" Compressed Sensing}},
  author = {Reeves, Galen and Gastpar, Michael},
  journal = {arXiv (Cornell University)},
  year = {2010},
  doi = {10.48550/arxiv.1001.4295}
}

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