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Signal recovery from random projections

Candès, Emmanuel and Romberg, Justin (2005) Signal recovery from random projections. In: Computational Imaging III. Proceedings of SPIE. No.5674. Society of Photo-optical Instrumentation Engineers (SPIE) , Bellingham, WA, pp. 76-86. ISBN 9780819456472. https://resolver.caltech.edu/CaltechAUTHORS:20190221-110530172

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Abstract

Can we recover a signal f∈R^N 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.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1117/12.600722DOIArticle
Additional Information:© 2005 Society of Photo-Optical Instrumentation Engineers (SPIE). This work was supported by NSF grants DMS 01-40698, DMS 01-40698 and ITR ACI-0204932.
Funders:
Funding AgencyGrant Number
NSFDMS 01-40698
NSFDMS 01-40698
NSFACI-0204932
Series Name:Proceedings of SPIE
Issue or Number:5674
Record Number:CaltechAUTHORS:20190221-110530172
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190221-110530172
Official Citation:Emmanuel J. Candes and Justin K. Romberg "Signal recovery from random projections", Proc. SPIE 5674, Computational Imaging III, (11 March 2005); doi: 10.1117/12.600722; https://doi.org/10.1117/12.600722
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:93163
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:22 Feb 2019 17:29
Last Modified:03 Oct 2019 20:51

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