The DOI matches its Crossref record; 43 of the 43 references it cites were found in a registry or an index.
An Augmented Lagrangian Approach to the Constrained Optimization Formulation of Imaging Inverse Problems
Open accessAbstract
We propose a new fast algorithm for solving one of the standard approaches to ill-posed linear inverse problems (IPLIP), where a (possibly nonsmooth) regularizer is minimized under the constraint that the solution explains the observations sufficiently well. Although the regularizer and constraint are usually convex, several particular features of these problems (huge dimensionality, nonsmoothness) preclude the use of off-the-shelf optimization tools and have stimulated a considerable amount of research. In this paper, we propose a new efficient algorithm to handle one class of constrained problems (often known as basis pursuit denoising) tailored to image recovery applications. The proposed algorithm, which belongs to the family of augmented Lagrangian methods, can be used to deal with a variety of imaging IPLIP, including deconvolution and reconstruction from compressive observations (such as MRI), using either total-variation or wavelet-based (or, more generally, frame-based) regularization. The proposed algorithm is an instance of the so-called alternating direction method of multipliers, for which convergence sufficient conditions are known; we show that these conditions are satisfied by the proposed algorithm. Experiments on a set of image restoration and reconstruction benchmark problems show that the proposed algorithm is a strong contender for the state-of-the-art.
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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
The Little Engine That Could: Regularization by Denoising (RED)
Romano, Y., Elad, M., & Milanfar, P. (2017) · SIAM Journal on Imaging Sciences · doi:10.1137/16m1102884 · Cited by 934
BM3D Frames and Variational Image Deblurring
Danielyan, A., Katkovnik, V., & Egiazarian, K. (2012) · IEEE Transactions on Image Processing · doi:10.1109/tip.2011.2176954 · Cited by 611
Fast $\ell_{1}$-Minimization Algorithms for Robust Face Recognition
Yang, A. Y., Zhou, Z., Balasubramanian, A. G., Sastry, S. S., & Ma, Y. (2013) · IEEE Transactions on Image Processing · doi:10.1109/tip.2013.2262292 · Cited by 341
Representer Theorems for Sparsity-Promoting $\ell _{1}$ Regularization
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Metadata
- Authors
- Afonso, M. V., Bioucas-Dias, J. M., & Figueiredo, M. A. T.
- Venue
- IEEE Transactions on Image Processing
- Published
- 2011-03
- Volume
- 20
- Issue
- 3
- Pages
- 681-695
- ISSN
- 1057-7149 (ISSN-L)
- 1941-0042
- OpenAlex
- W2123031198
- Cited by
- 938
- References
- 43
- FWCI
- 37.22
- Type
- journal article
- Language
- en
- Open access
- green
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