The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.
The Split Bregman Method for L1-Regularized Problems
Abstract
The class of L1-regularized optimization problems has received much attention recently because of the introduction of “compressed sensing,” which allows images and signals to be reconstructed from small amounts of data. Despite this recent attention, many L1-regularized problems still remain difficult to solve, or require techniques that are very problem-specific. In this paper, we show that Bregman iteration can be used to solve a wide variety of constrained optimization problems. Using this technique, we propose a “split Bregman” method, which can solve a very broad class of L1-regularized problems. We apply this technique to the Rudin–Osher–Fatemi functional for image denoising and to a compressed sensing problem that arises in magnetic resonance imaging.
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Cites
Boyd, S., & Vandenberghe, L. (2004) · doi:10.1017/cbo9780511804441 · Cited by 56,601
Fast approximate energy minimization via graph cuts
Boykov, Y., Veksler, O., & Zabih, R. (2001) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.969114 · Cited by 6,988
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
Deep Convolutional Neural Network for Inverse Problems in Imaging
Jin, K. H., McCann, M. T., Froustey, E., & Unser, M. (2017) · IEEE Transactions on Image Processing · doi:10.1109/tip.2017.2713099 · Cited by 2,529
“compressed sensing [7] and the related regularizers such as total variation [1], [2], [4], [8], robust and practical algorithms”
BackgroundMethodMagnetic resonance fingerprinting
Ma, D., Gulani, V., Seiberlich, N., Liu, K., Sunshine, J. L., Duerk, J. L., & Griswold, M. A. (2013) · Nature · doi:10.1038/nature11971 · Cited by 1,577
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
Plug-and-Play priors for model based reconstruction
Venkatakrishnan, S. V., Bouman, C. A., & Wohlberg, B. (2013) · 2013 IEEE Global Conference on Signal and Information Processing · doi:10.1109/globalsip.2013.6737048 · Cited by 1,178
Metadata
- Authors
- Goldstein, T., & Osher, S.
- Venue
- SIAM Journal on Imaging Sciences
- Published
- 2009-01
- Volume
- 2
- Issue
- 2
- Pages
- 323-343
- ISSN
- 1936-4954 (ISSN-L)
- OpenAlex
- W2142058898
- Cited by
- 4,282
- References
- 2
- FWCI
- 162.90
- Type
- journal article
- Language
- en
- Open access
- closed
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