Algorithms for structured sparsity promoting functions regularized image restoration model

• Published in: Sampling theory, signal processing, and data analysis Vol. 23; no. 2
• Main Authors: Prater-Bennette, Ashley, Shen, Lixin, Tripp, Erin E., Wei, Jianchen
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.12.2025
• Subjects: Abstract Harmonic Analysis; Machine Learning; Mathematics; Mathematics and Statistics; Original Article; Signal,Image and Speech Processing; 68U10; Difference of convex algorithms; 94A08; 65F22; Proximity operator; 90C26; Image restoration; Sparsity promoting function; 46N10
• ISSN: 2730-5716; 2730-5724
• DOI: 10.1007/s43670-025-00102-7

In the realm of image processing and analysis, image restoration stands out as a pivotal area, addressing the challenge of reconstructing degraded or distorted images. Typically categorized as an inverse problem, image restoration often leverages regularization techniques to enhance the quality of reconstructed images. This paper introduces an image restoration model that incorporates regularization through structured sparsity promoting functions (SPFs). The proposed model’s objective function structure is a key aspect, prompting the exploration of various formulations conducive to the application of existing algorithms. Among the algorithms considered are the inertial proximal algorithm for nonconvex optimization (iPiano), difference of convex algorithm (DCA), proximal linearized DCA, proximal DCA with extrapolation, double-proximal gradient algorithm, and the alternating direction method of multipliers (ADMM). To facilitate algorithmic application, the objective function is reformulated in multiple ways, ensuring compatibility with the diverse optimization approaches mentioned above. The comparative analysis of these algorithms serves as a benchmark for evaluating their performance concerning the proposed image restoration model. This study contributes to the understanding of the effectiveness of different optimization strategies in the context of structured sparsity promoting functions for image restoration.