ORIGINAL RESEARCH article
Front. Big Data
Sec. Data Mining and Management
This article is part of the Research TopicMachine Learning for Large-Scale Data Processing: Algorithms and ApplicationsView all articles
M-PSGP: A momentum-based proximal scaled gradient projection algorithm for nonsmooth optimization with application to image deblurring
Provisionally accepted
- Chongqing University, Chongqing, China
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In this paper, we focus on investigating the nonsmooth convex optimization problem with l1-norm under the non-negative constraint, with the aim of developing an inverse problem solver for image deblurring. The research on solving this problem has garnered extensive attention and exerted a significant impact on image processing fields. Nevertheless, related optimization algorithms usually suffer from overfitting and slow convergence, especially in the presence of ill-conditioned data or noise. In response to these challenges, we propose a momentum-based proximal scaled gradient projection (M-PSGP) algorithm. The M-PSGP algorithm, which is based on the proximal operator and scaled gradient projection (SGP) algorithm, integrates an improved Barzilai-Borwein-like step-size selection rule and a unified momentum acceleration framework, to achieve a balance between performance optimization and convergence rate. Numerical experiments demonstrate the superiority of the M-PSGP algorithm by comparing with other seminal algorithms in image deblurring tasks, and manifest the significance of our improved step-size and momentum acceleration framework in enhancing convergence properties.
Keywords: Momentum acceleration, Adaptive step-size, Barzilai–Borwein rules, Proximal gradient descent, nonsmooth constrainedoptimization
Received: 12 Sep 2025; Accepted: 03 Nov 2025.
Copyright: © 2025 Ning, Lü and Liao. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence:
Qingguo Lü, lvqingguo886@126.com
Xiaofeng Liao, xfliao2025@126.com
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