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Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
Abstract
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$ {\rm O}(m \ln d)$random linear measurements of that signal. This is a massive improvement over previous results, which require${\rm 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.
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Cited by
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Candes, E. J., & Wakin, M. B. (2008) · IEEE Signal Processing Magazine · doi:10.1109/msp.2007.914731 · Cited by 10,017
Discovering governing equations from data by sparse identification of nonlinear dynamical systems
Brunton, S. L., Proctor, J. L., & Kutz, J. N. (2016) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1517384113 · Cited by 4,796
Ji, S., Xue, Y., & Carin, L. (2008) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2007.914345 · Cited by 2,406
Chen, C. L. P., & Liu, Z. (2018) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2017.2716952 · Cited by 1,957
Magnetic resonance fingerprinting
Ma, D., Gulani, V., Seiberlich, N., Liu, K., Sunshine, J. L., Duerk, J. L., & Griswold, M. A. (2013) · Nature · doi:10.1038/nature11971 · Cited by 1,577
Metadata
- Authors
- Tropp, J. A., & Gilbert, A. C.
- Venue
- IEEE Transactions on Information Theory
- Published
- 2007-12
- Volume
- 53
- Issue
- 12
- Pages
- 4655-4666
- ISSN
- 0018-9448 (ISSN-L)
- OpenAlex
- W2127271355
- Cited by
- 9,653
- References
- 2
- FWCI
- 198.70
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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