The DOI matches its Crossref record; 18 of the 18 references it cites were found in a registry or an index.
Signal recovery from random projections
Open accessAbstract
Can we recover a signal f∈RN from a small number of linear measurements? A series of recent papers developed a collection of results showing that it is surprisingly possible to reconstruct certain types of signals accurately from limited measurements. In a nutshell, suppose that f is compressible in the sense that it is well-approximated by a linear combination of M vectors taken from a known basis Ψ. Then not knowing anything in advance about the signal, f can (very nearly) be recovered from about M log N generic nonadaptive measurements only. The recovery procedure is concrete and consists in solving a simple convex optimization program. In this paper, we show that these ideas are of practical significance. Inspired by theoretical developments, we propose a series of practical recovery procedures and test them on a series of signals and images which are known to be well approximated in wavelet bases. We demonstrate that it is empirically possible to recover an object from about 3M-5M projections onto generically chosen vectors with an accuracy which is as good as that obtained by the ideal M-term wavelet approximation. We briefly discuss possible implications in the areas of data compression and medical imaging.
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Cites
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Self-citationDaubechies, I., & Heil, C. (1992) · Computers in Physics · doi:10.1063/1.4823127 · Cited by 15,631
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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-citationA new, fast, and efficient image codec based on set partitioning in hierarchical trees
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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
The Split Bregman Method for L1-Regularized Problems
Goldstein, T., & Osher, S. (2009) · SIAM Journal on Imaging Sciences · doi:10.1137/080725891 · Cited by 4,282
Lustig, M., Donoho, D. L., Santos, J. M., & Pauly, J. M. (2008) · IEEE Signal Processing Magazine · doi:10.1109/msp.2007.914728 · Cited by 2,246
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
Iterative Thresholding for Sparse Approximations
Blumensath, T., & Davies, M. E. (2008) · Journal of Fourier Analysis and Applications · doi:10.1007/s00041-008-9035-z · Cited by 1,248
Metadata
- Authors
- Candes, E. J., & Romberg, J. K.
- Venue
- SPIE Proceedings
- Publisher
- SPIE
- Published
- 2005-03-11
- Volume
- 5674
- Pages
- 76
- ISSN
- 0277-786X (ISSN-L)
- OpenAlex
- W2161409394
- Cited by
- 299
- References
- 18
- FWCI
- 21.10
- Type
- conference paper
- Language
- en
- Open access
- bronze
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
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.
