The DOI matches its Crossref record; 52 of the 52 references it cites were found in a registry or an index.
Majorization–Minimization Algorithms for Wavelet-Based Image Restoration
Abstract
Standard formulations of image/signal deconvolution under wavelet-based priors/regularizers lead to very high-dimensional optimization problems involving the following difficulties: the non-Gaussian (heavy-tailed) wavelet priors lead to objective functions which are nonquadratic, usually nondifferentiable, and sometimes even nonconvex; the presence of the convolution operator destroys the separability which underlies the simplicity of wavelet-based denoising. This paper presents a unified view of several recently proposed algorithms for handling this class of optimization problems, placing them in a common majorization-minimization (MM) framework. One of the classes of algorithms considered (when using quadratic bounds on nondifferentiable log-priors) shares the infamous "singularity issue" (SI) of "iteratively reweighted least squares" (IRLS) algorithms: the possibility of having to handle infinite weights, which may cause both numerical and convergence issues. In this paper, we prove several new results which strongly support the claim that the SI does not compromise the usefulness of this class of algorithms. Exploiting the unified MM perspective, we introduce a new algorithm, resulting from using l1 bounds for nonconvex regularizers; the experiments confirm the superior performance of this method, when compared to the one based on quadratic majorization. Finally, an experimental comparison of the several algorithms, reveals their relative merits for different standard types of scenarios.
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Cited by
Enhancing Sparsity by Reweighted ℓ 1 Minimization
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A New TwIST: Two-Step Iterative Shrinkage/Thresholding Algorithms for Image Restoration
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Self-citationMajorization-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
Fast Image Recovery Using Variable Splitting and Constrained Optimization
Afonso, M. V., Bioucas-Dias, J. M., & Figueiredo, M. A. T. (2010) · IEEE Transactions on Image Processing · doi:10.1109/tip.2010.2047910 · Cited by 1,223
Self-citation
Metadata
- Authors
- Figueiredo, M. A. T., Bioucas-Dias, J. M., & Nowak, R. D.
- Venue
- IEEE Transactions on Image Processing
- Published
- 2007-12
- Volume
- 16
- Issue
- 12
- Pages
- 2980-2991
- ISSN
- 1057-7149 (ISSN-L)
- 1941-0042
- OpenAlex
- W1975377467
- Cited by
- 548
- References
- 52
- FWCI
- 27.93
- Type
- journal article
- Language
- en
- Open access
- closed
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