ArticleSIAM journal on imaging sciences2026
Smooth optimization using global and local low-rank regularizers.
Article in SIAM journal on imaging sciences, 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 2 papers.
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Who cites it
2 citing papers in PubMed.
- ALPCAHUS: Subspace Clustering for Heteroscedastic Data.IEEE transactions on signal processing : a publication of the IEEE Signal Processing Society · 2026Article
- Spatiotemporal Maps for Dynamic MRI Reconstruction.IEEE transactions on computational imaging · 2026Article
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Authors and funding
4 authors.
Funding
Abstract
Many inverse problems and signal processing problems involve low-rank regularizers based on the nuclear norm. Commonly, proximal gradient methods (PGM) are adopted to solve this type of non-smooth problems as they can offer fast and guaranteed convergence. However, PGM methods cannot be simply applied in settings where low-rank models are imposed locally on overlapping patches; therefore, heuristic approaches have been proposed that lack convergence guarantees. In this work we propose to replace the nuclear norm with a smooth approximation in which a Huber-type function is applied to each singular value. By providing a theoretical framework based on singular value function theory, we show that important properties can be established for the proposed regularizer, such as: convexity, differentiability, and Lipschitz continuity of the gradient. Moreover, we provide a closed-form expression for the regularizer gradient, enabling the use of standard iterative gradient-based optimization algorithms (
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