Signal recovery from random projections
- Creators
- Candès, Emmanuel
- Romberg, Justin
- Others:
- Bouman, Charles A.
- Miller, Eric L.
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.
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.Attached Files
Published - 76.pdf
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Additional details
- Eprint ID
- 93163
- Resolver ID
- CaltechAUTHORS:20190221-110530172
- DMS 01-40698
- NSF
- DMS 01-40698
- NSF
- ACI-0204932
- NSF
- Created
-
2019-02-22Created from EPrint's datestamp field
- Updated
-
2021-11-16Created from EPrint's last_modified field
- Series Name
- Proceedings of SPIE
- Series Volume or Issue Number
- 5674