"Compressed" compressed sensing

Published

Journal Article

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. © 2010 IEEE.

Full Text

Duke Authors

Cited Authors

  • Reeves, G; Gastpar, M

Published Date

  • August 23, 2010

Published In

  • Ieee International Symposium on Information Theory Proceedings

Start / End Page

  • 1548 - 1552

Digital Object Identifier (DOI)

  • 10.1109/ISIT.2010.5513517

Citation Source

  • Scopus