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Proceedings Article

Signal recovery from random projections

[+] Author Affiliations
Emmanuel J. Candes, Justin K. Romberg

California Institute of Technology (USA)

Proc. SPIE 5674, Computational Imaging III, 76 (March 31, 2005); doi:10.1117/12.600722
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From Conference Volume 5674

  • Computational Imaging III
  • Charles A. Bouman; Eric L. Miller
  • San Jose, CA | January 17, 2005

abstract

Can we recover a signal f ∈RN from a small number of linear measurements? A series of recent papers developed a collection of results showing that it is surprisingly possible to reconstruct certain types of signals accurately from limited measurements. In a nutshell, suppose that f is compressible in the sense that it is well-approximated by a linear combination of M vectors taken from a known basis Ψ. Then not knowing anything in advance about the signal, f can (very nearly) be recovered from about M log N generic nonadaptive measurements only. The recovery procedure is concrete and consists in solving a simple convex optimization program. In this paper, we show that these ideas are of practical significance. Inspired by theoretical developments, we propose a series of practical recovery procedures and test them on a series of signals and images which are known to be well approximated in wavelet bases. We demonstrate that it is empirically possible to recover an object from about 3M -5M projections onto generically chosen vectors with an accuracy which is as good as that obtained by the ideal M -term wavelet approximation. We briefly discuss possible implications in the areas of data compression and medical imaging.

© (2005) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
Citation

Emmanuel J. Candes and Justin K. Romberg
"Signal recovery from random projections", Proc. SPIE 5674, Computational Imaging III, 76 (March 31, 2005); doi:10.1117/12.600722; http://dx.doi.org/10.1117/12.600722


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