Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit

This paper demonstrates theoretically and empirically that a greedy algorithm called orthogonal matching pursuit (OMP) can reliably recover a signal with m nonzero entries in dimension d given O(m ln d) random linear measurements of that signal. This is a massive improvement over previous results, w...

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Bibliographic Details
Published inIEEE transactions on information theory Vol. 53; no. 12; pp. 4655 - 4666
Main Authors Tropp, J.A., Gilbert, A.C.
Format Journal Article
LanguageEnglish
Published New York, NY IEEE 01.12.2007
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Algorithms
Applied sciences
approximation
Back propagation
basis pursuit
Blood
Compressed sensing
Detection, estimation, filtering, equalization, prediction
Dimensional measurements
Electrical engineering
Electronics
Empirical analysis
Exact sciences and technology
Greedy algorithms
group testing
Information theory
Information, signal and communications theory
Matching
Matching pursuit algorithms
Mathematics
Measurement
Miscellaneous
orthogonal matching pursuit
Performance evaluation
Recovery
Reliability theory
Signal and communications theory
Signal processing
signal recovery
Signal, noise
sparse approximation
Telecommunications and information theory
Testing
Vectors
approximation
compressed sensing
Iterative method
signal recovery
basis pursuit
Implementation
orthogonal matching pursuit
Signal restoration
Algorithms
group testing
Matching pursuit
Greedy algorithm
Signal processing
sparse approximation
Sparse representation
Signal reconstruction
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Summary:This paper demonstrates theoretically and empirically that a greedy algorithm called orthogonal matching pursuit (OMP) can reliably recover a signal with m nonzero entries in dimension d given O(m ln d) random linear measurements of that signal. This is a massive improvement over previous results, which require O (m 2 ) measurements. The new results for OMP are comparable with recent results for another approach called basis pursuit (BP). In some settings, the OMP algorithm is faster and easier to implement, so it is an attractive alternative to BP for signal recovery problems.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2007.909108