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arXiv · 2607.10864

Multilevel Preconditioning Strategies for Convex Optimization Methods in Image Deblurring

Stefano Aleotti·Claudia Binda·Marco Donatelli·Rolf Krause
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Abstract

Proximal gradient methods are widely used in imaging, and their speed of convergence can be accelerated by incorporating variable metrics and/or extrapolation steps. Recent works have shown that preconditioning strategies can significantly enhance this acceleration, in particular, for image deblurring problems. In parallel, a multilevel framework has been introduced to speed up inertial and inexact forward-backward schemes for image restoration problems. In this paper, we combine preconditioning and multilevel strategies to design a robust and consistent acceleration framework for both standard and inexact forward-backward schemes applied to regularized convex optimization problems. Numerical experiments in image deblurring confirm that our approach yields a substantial improvement in convergence speed compared to standard methods.

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Stefano Aleotti, Claudia Binda, Marco Donatelli, Rolf Krause. 2026-07-12. Multilevel Preconditioning Strategies for Convex Optimization Methods in Image Deblurring. https://arxiv.org/abs/2607.10864

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