The DOI matches its Crossref record; 25 of the 25 references it cites were found in a registry or an index.
Signal Reconstruction From Noisy Random Projections
Abstract
Recent results show that a relatively small number of random projections of a signal can contain most of its salient information. It follows that if a signal is compressible in some orthonormal basis, then a very accurate reconstruction can be obtained from random projections. This "compressive sampling" approach is extended here to show that signals can be accurately recovered from random projections contaminated with noise. A practical iterative algorithm for signal reconstruction is proposed, and potential applications to coding, analog-digital (A/D) conversion, and remote wireless sensing are discussed
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Cites
Elements of Information Theory
Cover, T. M., & Thomas, J. A. (2001) · Wiley eBooks · doi:10.1002/0471200611 · Cited by 36,808
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
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
An iterative thresholding algorithm for linear inverse problems with a sparsity constraint.
Daubechies, I., Defrise, M., & De Mol, C. (2004) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.20042 · Cited by 4,958
The Dantzig selector: Statistical estimation when p is much larger than n
Candes, E., & Tao, T. (2007) · The Annals of Statistics · doi:10.1214/009053606000001523 · Cited by 1,747
An EM algorithm for wavelet-based image restoration
Figueiredo, M. A. T., & Nowak, R. D. (2003) · IEEE Transactions on Image Processing · doi:10.1109/tip.2003.814255 · Cited by 1,219
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Cited by
An Introduction To Compressive Sampling
Candes, E. J., & Wakin, M. B. (2008) · IEEE Signal Processing Magazine · doi:10.1109/msp.2007.914731 · Cited by 10,017
Sparse MRI: The application of compressed sensing for rapid MR imaging
Lustig, M., Donoho, D., & Pauly, J. M. (2007) · Magnetic Resonance in Medicine · doi:10.1002/mrm.21391 · Cited by 6,952
Ji, S., Xue, Y., & Carin, L. (2008) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2007.914345 · Cited by 2,406
Sparsity and incoherence in compressive sampling
Candès, E., & Romberg, J. (2007) · Inverse Problems · doi:10.1088/0266-5611/23/3/008 · Cited by 2,075
Model-Based Compressive Sensing
Baraniuk, R. G., Cevher, V., Duarte, M. F., & Hegde, C. (2010) · IEEE Transactions on Information Theory · doi:10.1109/tit.2010.2040894 · Cited by 1,308
Metadata
- Authors
- Haupt, J., & Nowak, R.
- Venue
- IEEE Transactions on Information Theory
- Published
- 2006-09
- Volume
- 52
- Issue
- 9
- Pages
- 4036-4048
- ISSN
- 0018-9448 (ISSN-L)
- OpenAlex
- W2154304330
- Cited by
- 608
- References
- 25
- FWCI
- 61.75
- Type
- journal article
- Language
- en
- Open access
- closed
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