The DOI matches its Crossref record; 3 of the 3 references it cites were found in a registry or an index.
Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing
Abstract
We propose simple and extremely efficient methods for solving the basis pursuit problem $\min\{\|u\|_1 : Au = f, u\in\mathbb{R}^n\},$ which is used in compressed sensing. Our methods are based on Bregman iterative regularization, and they give a very accurate solution after solving only a very small number of instances of the unconstrained problem $\min_{u\in\mathbb{R}^n} \mu\|u\|_1+\frac{1}{2}\|Au-f^k\|_2^2$ for given matrix A and vector $f^k$. We show analytically that this iterative approach yields exact solutions in a finite number of steps and present numerical results that demonstrate that as few as two to six iterations are sufficient in most cases. Our approach is especially useful for many compressed sensing applications where matrix-vector operations involving A and $A^\top$ can be computed by fast transforms. Utilizing a fast fixed-point continuation solver that is based solely on such operations for solving the above unconstrained subproblem, we were able to quickly solve huge instances of compressed sensing problems on a standard PC.
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Cites
Regression shrinkage and selection via the lasso
Tibshirani, R. (1996) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1996.tb02080.x · Cited by 51,482
Exact Reconstruction of Sparse Signals via Nonconvex Minimization
Chartrand, R. (2007) · IEEE Signal Processing Letters · doi:10.1109/lsp.2007.898300 · Cited by 1,277
Analog-to-Information Conversion via Random Demodulation
Kirolos, S., Laska, J., Wakin, M., Duarte, M., Baron, D., Ragheb, T., Massoud, Y., & Baraniuk, R. (2006) · 2006 IEEE Dallas/CAS Workshop on Design, Applications, Integration and Software · doi:10.1109/dcas.2006.321036 · Cited by 393
Cited by
Boyd, S., Parikh, N., Chu, E., Peleato, B., & Eckstein, J. (2011) · Foundations and Trends® in Machine Learning · doi:10.1561/2200000016 · Cited by 17,075
Fast Image Recovery Using Variable Splitting and Constrained Optimization
Afonso, M. V., Bioucas-Dias, J. M., & Figueiredo, M. A. T. (2010) · IEEE Transactions on Image Processing · doi:10.1109/tip.2010.2047910 · Cited by 1,223
Blind deconvolution using a normalized sparsity measure
Krishnan, D., Tay, T., & Fergus, R. (2011) · CVPR 2011 · doi:10.1109/cvpr.2011.5995521 · Cited by 1,119
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
On the Convergence of Decentralized Gradient Descent
Yuan, K., Ling, Q., & Yin, W. (2013) · arXiv · doi:10.48550/arxiv.1310.7063 · Cited by 635
Self-citationMultimodal Deep Learning Approach for Joint EEG-EMG Data Compression and Classification
Ben Said, A., Mohamed, A., Elfouly, T., Harras, K., & Wang, Z. J. (2017) · 2017 IEEE Wireless Communications and Networking Conference (WCNC) · doi:10.1109/wcnc.2017.7925709 · Cited by 86
SPEED: A Deep Learning Assisted Privacy-Preserved Framework for Intelligent Transportation Systems
Usman, M., Jan, M. A., & Jolfaei, A. (2021) · IEEE Transactions on Intelligent Transportation Systems · doi:10.1109/tits.2020.3031721 · Cited by 32
Sparsity-Aware Learning and Compressed Sensing: An Overview
Theodoridis, S., Kopsinis, Y., & Slavakis, K. (2014) · Academic Press Library in Signal Processing · doi:10.1016/b978-0-12-396502-8.00023-1 · Cited by 14
Metadata
- Authors
- Yin, W., Osher, S., Goldfarb, D., & Darbon, J.
- Venue
- SIAM Journal on Imaging Sciences
- Published
- 2008-01
- Volume
- 1
- Issue
- 1
- Pages
- 143-168
- ISSN
- 1936-4954 (ISSN-L)
- OpenAlex
- W1996287810
- Cited by
- 1,414
- References
- 3
- FWCI
- 78.07
- Type
- journal article
- Language
- en
- Open access
- closed
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