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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
Conic Optimization via Operator Splitting and Homogeneous Self-Dual Embedding
O’Donoghue, B., Chu, E., Parikh, N., & Boyd, S. (2016) · Journal of Optimization Theory and Applications · doi:10.1007/s10957-016-0892-3 · Cited by 664
Tadano, T., & Tsuneyuki, S. (2015) · Physical Review B · doi:10.1103/physrevb.92.054301 · Cited by 640
Image super-resolution: the techniques, applications, and future
Yue, L., Shen, H., Li, J., Yuan, Q., Zhang, H., & Zhang, L. (2016) · Signal Processing · doi:10.1016/j.sigpro.2016.05.002 · Cited by 554
Robust Multichannel Blind Deconvolution via Fast Alternating Minimization
Sroubek, F., & Milanfar, P. (2012) · IEEE Transactions on Image Processing · doi:10.1109/tip.2011.2175740 · Cited by 180
Object Detection and Classification by Decision-Level Fusion for Intelligent Vehicle Systems
Oh, S.-I., & Kang, H.-B. (2017) · Sensors · doi:10.3390/s17010207 · Cited by 120
SuRVoS: Super-Region Volume Segmentation workbench
Luengo, I., Darrow, M. C., Spink, M. C., Sun, Y., Dai, W., He, C. Y., Chiu, W., Pridmore, T., Ashton, A. W., Duke, E. M. H., et al. (2017) · Journal of Structural Biology · doi:10.1016/j.jsb.2017.02.007 · Cited by 89
Representer Theorems for Sparsity-Promoting $\ell _{1}$ Regularization
Unser, M., Fageot, J., & Gupta, H. (2016) · IEEE Transactions on Information Theory · doi:10.1109/tit.2016.2590421 · Cited by 36
Local‐ and Global‐Statistics‐Based Active Contour Model for Image Segmentation
Wu, B., & Yang, Y. (2012) · Mathematical Problems in Engineering · doi:10.1155/2012/791958 · Cited by 30
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
Magnetic imaging and machine vision NDT for the on-line inspection of stainless steel strips
Ricci, M., Ficola, A., Fravolini, M. L., Battaglini, L., Palazzi, A., Burrascano, P., Valigi, P., Appolloni, L., Cervo, S., & Rocchi, C. (2013) · Measurement Science and Technology · doi:10.1088/0957-0233/24/2/025401 · Cited by 11
Augmented distributed optimization for networked systems
Xu, J. (2019) · doi:10.32657/10356/68805 · Cited by 5
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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