The DOI matches its Crossref record; 21 of the 21 references it cites were found in a registry or an index.
Signal Recovery From Incomplete and Inaccurate Measurements Via Regularized Orthogonal Matching Pursuit
Open accessAbstract
We demonstrate a simple greedy algorithm that can reliably recover a vectorv¿ ¿dfrom incomplete and inaccurate measurementsx= ¿v+e. Here, ¿ is aNxdmeasurement matrix withNeis an error vector. Our algorithm, Regularized Orthogonal Matching Pursuit (ROMP), seeks to provide the benefits of the two major approaches to sparse recovery. It combines the speed and ease of implementation of the greedy methods with the strong guarantees of the convex programming methods. For any measurement matrix ¿ that satisfies a quantitative restricted isometry principle, ROMP recovers a signalvwithO(n) nonzeros from its inaccurate measurementsxin at mostniterations, where each iteration amounts to solving a least squares problem. The noise level of the recovery is proportional to ¿{logn} ||e||2. In particular, if the error termevanishes the reconstruction is exact.
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Cites
Donoho, D. L. (2006) · IEEE Transactions on Information Theory · doi:10.1109/tit.2006.871582 · Cited by 23,994
Donoho, D. L. (2004) · Cited by 16,703
Candes, E. J., Romberg, J., & Tao, T. (2006) · IEEE Transactions on Information Theory · doi:10.1109/tit.2005.862083 · Cited by 15,639
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
Tropp, J. A., & Gilbert, A. C. (2007) · IEEE Transactions on Information Theory · doi:10.1109/tit.2007.909108 · Cited by 9,653
Decoding by Linear Programming
Candes, E. J., & Tao, T. (2005) · IEEE Transactions on Information Theory · doi:10.1109/tit.2005.858979 · Cited by 7,121
Stable signal recovery from incomplete and inaccurate measurements
Candès, E. J., Romberg, J. K., & Tao, T. (2006) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.20124 · Cited by 7,036
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
Candes, E. J., & Tao, T. (2006) · IEEE Transactions on Information Theory · doi:10.1109/tit.2006.885507 · Cited by 6,839
CoSaMP: Iterative signal recovery from incomplete and inaccurate samples
Needell, D., & Tropp, J. A. (2009) · Applied and Computational Harmonic Analysis · doi:10.1016/j.acha.2008.07.002 · Cited by 4,326
Self-citationThe restricted isometry property and its implications for compressed sensing
Candès, E. J. (2008) · Comptes Rendus. Mathématique · doi:10.1016/j.crma.2008.03.014 · Cited by 3,686
Figueiredo, M. A. T., Nowak, R. D., & Wright, S. J. (2007) · IEEE Journal of Selected Topics in Signal Processing · doi:10.1109/jstsp.2007.910281 · Cited by 3,524
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Subspace Pursuit for Compressive Sensing Signal Reconstruction
Dai, W., & Milenkovic, O. (2009) · IEEE Transactions on Information Theory · doi:10.1109/tit.2009.2016006 · Cited by 2,388
Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals
Tropp, J. A., Laska, J. N., Duarte, M. F., Romberg, J. K., & Baraniuk, R. G. (2010) · IEEE Transactions on Information Theory · doi:10.1109/tit.2009.2034811 · Cited by 1,089
Computational Methods for Sparse Solution of Linear Inverse Problems
Tropp, J. A., & Wright, S. J. (2010) · Proceedings of the IEEE · doi:10.1109/jproc.2010.2044010 · Cited by 1,046
Advances on Spectrum Sensing for Cognitive Radio Networks: Theory and Applications
Ali, A., & Hamouda, W. (2017) · IEEE Communications Surveys & Tutorials · doi:10.1109/comst.2016.2631080 · Cited by 624
Dense Error Correction Via $\ell^1$-Minimization
Wright, J., & Ma, Y. (2010) · IEEE Transactions on Information Theory · doi:10.1109/tit.2010.2048473 · Cited by 305
Metadata
- Authors
- Needell, D., & Vershynin, R.
- Venue
- IEEE Journal of Selected Topics in Signal Processing
- Published
- 2010-04
- Volume
- 4
- Issue
- 2
- Pages
- 310-316
- ISSN
- 1932-4553 (ISSN-L)
- 1941-0484
- OpenAlex
- W2095978736
- Cited by
- 850
- References
- 21
- FWCI
- 57.48
- Type
- journal article
- Language
- en
- Open access
- green
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