The DOI matches its Crossref record; 50 of the 50 references it cites were found in a registry or an index.
A Fast Algorithm for Sparse Reconstruction Based on Shrinkage, Subspace Optimization, and Continuation
Abstract
We propose a fast algorithm for solving the $\ell_1$-regularized minimization problem $\min_{x\in\mathbb{R}^n}\mu\|x\|_1+\|Ax-b\|^2_2$ for recovering sparse solutions to an undetermined system of linear equations $Ax=b$. The algorithm is divided into two stages that are performed repeatedly. In the first stage a first-order iterative “shrinkage” method yields an estimate of the subset of components of x likely to be nonzero in an optimal solution. Restricting the decision variables x to this subset and fixing their signs at their current values reduces the $\ell_1$-norm $\|x\|_1$ to a linear function of x. The resulting subspace problem, which involves the minimization of a smaller and smooth quadratic function, is solved in the second phase. Our code FPC_AS embeds this basic two-stage algorithm in a continuation (homotopy) approach by assigning a decreasing sequence of values to $\mu$. This code exhibits state-of-the-art performance in terms of both its speed and its ability to recover sparse signals.
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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
(2021) · A First Course in Statistical Programming with R · doi:10.1017/9781108993456.011 · Cited by 13,724
Matching pursuits with time-frequency dictionaries
Mallat, S. G., & Zhang, Z. (1993) · IEEE Transactions on Signal Processing · doi:10.1109/78.258082 · Cited by 9,112
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
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
Benchmarking optimization software with performance profiles
Dolan, E. D., & Moré, J. J. (2002) · Mathematical Programming · doi:10.1007/s101070100263 · Cited by 4,412
CoSaMP: Iterative signal recovery from incomplete and inaccurate samples
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Ma, S., Goldfarb, D., & Chen, L. (2011) · Mathematical Programming · doi:10.1007/s10107-009-0306-5 · Cited by 1,048
Self-citationComputational 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
NESTA: A Fast and Accurate First-Order Method for Sparse Recovery
Becker, S., Bobin, J., & Candès, E. J. (2011) · SIAM Journal on Imaging Sciences · doi:10.1137/090756855 · Cited by 848
Templates for convex cone problems with applications to sparse signal recovery
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Minimization of $\ell_{1-2}$ for Compressed Sensing
Yin, P., Lou, Y., He, Q., & Xin, J. (2015) · SIAM Journal on Scientific Computing · doi:10.1137/140952363 · Cited by 473
Metadata
- Authors
- Wen, Z., Yin, W., Goldfarb, D., & Zhang, Y.
- Venue
- SIAM Journal on Scientific Computing
- Published
- 2010-01
- Volume
- 32
- Issue
- 4
- Pages
- 1832-1857
- ISSN
- 1064-8275 (ISSN-L)
- 1095-7197
- OpenAlex
- W2022611944
- Cited by
- 280
- References
- 50
- FWCI
- 19.27
- Type
- journal article
- Language
- en
- Open access
- closed
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