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Signal recovery from random projections
- Source :
- Computational Imaging
- Publication Year :
- 2005
- Publisher :
- Society of Photo-optical Instrumentation Engineers (SPIE), 2005.
-
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 3 M -5 M 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.
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Computational Imaging
- Accession number :
- edsair.doi.dedup.....f2e1cd145135468b8d4d89ad52114212