The DOI matches its Crossref record; 51 of the 51 references it cites were found in a registry or an index.
A Unified Primal-Dual Algorithm Framework Based on Bregman Iteration
Open accessAbstract
In this paper, we propose a unified primal-dual algorithm framework for two classes of problems that arise from various signal and image processing applications. We also show the connections to existing methods, in particular Bregman iteration (Osher et al., Multiscale Model. Simul. 4(2):460–489, 2005) based methods, such as linearized Bregman (Osher et al., Commun. Math. Sci. 8(1):93–111, 2010; Cai et al., SIAM J. Imag. Sci. 2(1):226–252, 2009, CAM Report 09-28, UCLA, March 2009; Yin, CAAM Report, Rice University, 2009) and split Bregman (Goldstein and Osher, SIAM J. Imag. Sci., 2, 2009). The convergence of the general algorithm framework is proved under mild assumptions. The applications to ℓ 1 basis pursuit, TV−L 2 minimization and matrix completion are demonstrated. Finally, the numerical examples show the algorithms proposed are easy to implement, efficient, stable and flexible enough to cover a wide variety of applications.
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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
Nonlinear total variation based noise removal algorithms
Rudin, L. I., Osher, S., & Fatemi, E. (1992) · Physica D: Nonlinear Phenomena · doi:10.1016/0167-2789(92)90242-f · Cited by 15,704
Self-citationCandes, E. J., Romberg, J., & Tao, T. (2006) · IEEE Transactions on Information Theory · doi:10.1109/tit.2005.862083 · Cited by 15,639
Atomic Decomposition by Basis Pursuit
Chen, S. S., Donoho, D. L., & Saunders, M. A. (1998) · SIAM Journal on Scientific Computing · doi:10.1137/s1064827596304010 · Cited by 6,845
Principles of Computerized Tomographic Imaging
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A Singular Value Thresholding Algorithm for Matrix Completion
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Atomic Decomposition by Basis Pursuit
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An iterative thresholding algorithm for linear inverse problems with a sparsity constraint.
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Exact Matrix Completion via Convex Optimization
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Cited by
Parikh, N., & Boyd, S. (2014) · Foundations and Trends® in Optimization · doi:10.1561/2400000003 · Cited by 4,102
Condat, L. (2013) · Journal of Optimization Theory and Applications · doi:10.1007/s10957-012-0245-9 · Cited by 912
Parallel Multi-Block ADMM with o(1 / k) Convergence
Deng, W., Lai, M.-J., Peng, Z., & Yin, W. (2017) · Journal of Scientific Computing · doi:10.1007/s10915-016-0318-2 · Cited by 455
Metadata
- Authors
- Zhang, X., Burger, M., & Osher, S.
- Venue
- Journal of Scientific Computing
- Published
- 2010-08-05
- Volume
- 46
- Issue
- 1
- Pages
- 20-46
- ISSN
- 0885-7474 (ISSN-L)
- 1573-7691
- OpenAlex
- W2016910236
- Cited by
- 419
- References
- 51
- FWCI
- 25.27
- Type
- journal article
- Language
- en
- Open access
- hybrid
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