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Second-order Cone Programming Methods for Total Variation-Based Image Restoration
Abstract
In this paper we present optimization algorithms for image restoration based on the total variation (TV) minimization framework of Rudin, Osher, and Fatemi (ROF). Our approach formulates TV minimization as a second-order cone program which is then solved by interior-point algorithms that are efficient both in practice (using nested dissection and domain decomposition) and in theory (i.e., they obtain solutions in polynomial time). In addition to the original ROF minimization model, we show how to apply our approach to other TV models, including ones that are not solvable by PDE-based methods. Numerical results on a varied set of images are presented to illustrate the effectiveness of our approach.
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Cited by
Stable signal recovery from incomplete and inaccurate measurements
Candès, E. J., Romberg, J. K., & Tao, T. (2006) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.20124 · Cited by 7,036
Enhancing Sparsity by Reweighted ℓ 1 Minimization
Candès, E. J., Wakin, M. B., & Boyd, S. P. (2008) · Journal of Fourier Analysis and Applications · doi:10.1007/s00041-008-9045-x · Cited by 4,863
A New Alternating Minimization Algorithm for Total Variation Image Reconstruction
Wang, Y., Yang, J., Yin, W., & Zhang, Y. (2008) · SIAM Journal on Imaging Sciences · doi:10.1137/080724265 · Cited by 1,975
Self-citationAn Iterative Regularization Method for Total Variation-Based Image Restoration
Osher, S., Burger, M., Goldfarb, D., Xu, J., & Yin, W. (2005) · Multiscale Modeling & Simulation · doi:10.1137/040605412 · Cited by 1,787
Self-citationEsser, E., Zhang, X., & Chan, T. F. (2010) · SIAM Journal on Imaging Sciences · doi:10.1137/09076934x · Cited by 695
Metadata
- Authors
- Goldfarb, D., & Yin, W.
- Venue
- SIAM Journal on Scientific Computing
- Published
- 2005-01
- Volume
- 27
- Issue
- 2
- Pages
- 622-645
- ISSN
- 1064-8275 (ISSN-L)
- 1095-7197
- OpenAlex
- W2061979078
- Cited by
- 196
- References
- 0
- FWCI
- 19.55
- Type
- journal article
- Language
- en
- Open access
- closed
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