The DOI matches its Crossref record; 38 of the 38 references it cites were found in a registry or an index.
A Probabilistic and RIPless Theory of Compressed Sensing
Abstract
This paper introduces a simple and very general theory of compressive sensing. In this theory, the sensing mechanism simply selects sensing vectors independently at random from a probability distributionF; it includes all standard models-e.g., Gaussian, frequency measurements-discussed in the literature, but also provides a framework for new measurement strategies as well. We prove that if the probability distributionFobeys a simple incoherence property and an isotropy property, one can faithfully recover approximately sparse signals from a minimal number of noisy measurements. The novelty is that our recovery results do not require the restricted isometry property (RIP) to hold near the sparsity level in question, nor a random model for the signal. As an example, the paper shows that a signal withsnonzero entries can be faithfully recovered from aboutslognFourier coefficients that are contaminated with noise.
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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
Self-citationDecoding by Linear Programming
Candes, E. J., & Tao, T. (2005) · IEEE Transactions on Information Theory · doi:10.1109/tit.2005.858979 · Cited by 7,121
Self-citationStable 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
Self-citationJohnson, A. P. (2024) · Being and Becoming Teachers of Writing · doi:10.4324/9781003334798-34 · Cited by 4,502
The 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
Single-pixel imaging via compressive sampling
Duarte, M. F., Davenport, M. A., Takhar, D., Laska, J. N., Sun, T., Kelly, K. F., & Baraniuk, R. G. (2008) · IEEE Signal Processing Magazine · doi:10.1109/msp.2007.914730 · Cited by 3,575
Simultaneous analysis of Lasso and Dantzig selector
Bickel, P. J., Ritov, Y., & Tsybakov, A. B. (2009) · The Annals of Statistics · doi:10.1214/08-aos620 · Cited by 2,396
Cited by
Compressive fluorescence microscopy for biological and hyperspectral imaging
Studer, V., Bobin, J., Chahid, M., Mousavi, H. S., Candes, E., & Dahan, M. (2012) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1119511109 · Cited by 411
Self-citationSpatial Compressive Sensing for MIMO Radar
Rossi, M., Haimovich, A. M., & Eldar, Y. C. (2014) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2013.2289875 · Cited by 269
Ganguli, S., & Sompolinsky, H. (2012) · Annual Review of Neuroscience · doi:10.1146/annurev-neuro-062111-150410 · Cited by 256
BREAKING THE COHERENCE BARRIER: A NEW THEORY FOR COMPRESSED SENSING
ADCOCK, B., HANSEN, A. C., POON, C., & ROMAN, B. (2017) · Forum of Mathematics, Sigma · doi:10.1017/fms.2016.32 · Cited by 256
Gradient Coding Using the Stochastic Block Model
Charles, Z., & Papailiopoulos, D. (2018) · 2018 IEEE International Symposium on Information Theory (ISIT) · doi:10.1109/isit.2018.8437887 · Cited by 23
Metadata
- Authors
- Candes, E. J., & Plan, Y.
- Venue
- IEEE Transactions on Information Theory
- Published
- 2011-11
- Volume
- 57
- Issue
- 11
- Pages
- 7235-7254
- ISSN
- 0018-9448 (ISSN-L)
- 1557-9654
- OpenAlex
- W2137198385
- Cited by
- 598
- References
- 38
- FWCI
- 50.97
- 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).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
