The DOI matches its Crossref record; 3 of the 3 references it cites were found in a registry or an index.
Proximal Splitting Methods in Signal Processing
Abstract
The proximity operator of a convex function is a natural extension of the notion of a projection operator onto a convex set. This tool, which plays a central role in the analysis and the numerical solution of convex optimization problems, has recently been introduced in the arena of inverse problems and, especially, in signal processing, where it has become increasingly important. In this paper, we review the basic properties of proximity operators which are relevant to signal processing and present optimization methods based on these operators. These proximal splitting methods are shown to capture and extend several well-known algorithms in a unifying framework. Applications of proximal methods in signal recovery and synthesis are discussed.
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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
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
Beck, A., & Teboulle, M. (2009) · SIAM Journal on Imaging Sciences · doi:10.1137/080716542 · Cited by 11,952
A New TwIST: Two-Step Iterative Shrinkage/Thresholding Algorithms for Image Restoration
Bioucas-Dias, J. M., & Figueiredo, M. A. T. (2007) · IEEE Transactions on Image Processing · doi:10.1109/tip.2007.909319 · Cited by 2,064 · cited 1×
“Other variations of the forward-backward algorithm have al so been reported to yield improved convergence profiles [20,70,97,134,135].”
Background
Cited by
Parikh, N., & Boyd, S. (2014) · Foundations and Trends® in Optimization · doi:10.1561/2400000003 · Cited by 4,102
Majorization-Minimization Algorithms in Signal Processing, Communications, and Machine Learning
Sun, Y., Babu, P., & Palomar, D. P. (2017) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2016.2601299 · Cited by 1,820
TEASER: Fast and Certifiable Point Cloud Registration
Yang, H., Shi, J., & Carlone, L. (2021) · IEEE Transactions on Robotics · doi:10.1109/tro.2020.3033695 · Cited by 895
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
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
Metadata
- Authors
- Combettes, P. L., & Pesquet, J.-C.
- Venue
- Springer Optimization and Its Applications
- Publisher
- Springer New York
- Published
- 2011
- Pages
- 185-212
- ISSN
- 1931-6828 (ISSN-L)
- OpenAlex
- W1946620893
- Cited by
- 2,183
- References
- 3
- FWCI
- 291.87
- Type
- book chapter
- Language
- en
- Open access
- closed
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