Fast Image Recovery Using Variable Splitting and Constrained Optimization
Open accessAbstract
We propose a new fast algorithm for solving one of the standard formulations of image restoration and reconstruction which consists of an unconstrained optimization problem where the objective includes an l2 data-fidelity term and a nonsmooth regularizer. This formulation allows both wavelet-based (with orthogonal or frame-based representations) regularization or total-variation regularization. Our approach is based on a variable splitting to obtain an equivalent constrained optimization formulation, which is then addressed with an augmented Lagrangian method. The proposed algorithm is an instance of the so-called alternating direction method of multipliers, for which convergence has been proved. Experiments on a set of image restoration and reconstruction benchmark problems show that the proposed algorithm is faster than the current state of the art methods.
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Many other iterative methods for solving Eq. (5), including ADMM, FISTA, and SALSA, also rely on these basic building blocks.
“Many other iterate methods for solving Eq. (5), including ADMM [40], FISTA [41], and SALSA [42], also rely on these basic building blocks.”
From Deep Convolutional Neural Network for Inverse Problems in Imaging (2017) · cites this paper as [42]
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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 · see citing works
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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 · see citing works
“(5), including ADMM [40], FISTA [41], and SALSA [42], also rely on these basic building blocks.”
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 · see citing works
Plug-and-Play ADMM for Image Restoration: Fixed-Point Convergence and Applications
Chan, S. H., Wang, X., & Elgendy, O. A. (2017) · IEEE Transactions on Computational Imaging · doi:10.1109/tci.2016.2629286 · Cited by 904 · see citing works
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 · see citing works
FlexISP: a flexible camera image processing framework
Heide, F., Steinberger, M., Tsai, Y.-T., Rouf, M., Pająk, D., Reddy, D., Gallo, O., Liu, J., Heidrich, W., Egiazarian, K., et al. (2014) · ACM Transactions on Graphics · doi:10.1145/2661229.2661260 · Cited by 298 · see citing works
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 · see citing works
- Authors
- Afonso, M. V., Bioucas-Dias, J. M., & Figueiredo, M. A. T.
- Affiliations
- Instituto de Telecomunicações (PT)
- Venue
- IEEE Transactions on Image Processing
- Published
- 2010-09
- Volume
- 19
- Issue
- 9
- Pages
- 2345-2356
- ISSN
- 1057-7149 (ISSN-L)
- 1941-0042
- OpenAlex
- W2100705753
- Cited by
- 1,223
- References
- 1
- Citations by year
- 2026: 24 · 2025: 37 · 2024: 55 · 2023: 58 · 2022: 64 · 2021: 93 · 2020: 80 · 2019: 76 · 2018: 112 · 2017: 111 · 2016: 117 · 2015: 99 · 2014: 102 · 2013: 69 · 2012: 59
- FWCI
- 71.63
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- IEEE Transactions on Image Processing (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Image and Signal Denoising Methods
- Physical Sciences › Engineering › Computational Mechanics › Sparse and Compressive Sensing Techniques
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Optimization and Variational Analysis
- Keywords
- image restoration, image reconstruction, variable splitting, constrained optimization, augmented Lagrangian method, alternating direction method of multipliers, total variation regularization, frame representation, non-smooth regularization, convergence analysis
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