Novel forward–backward algorithms for optimization and applications to compressive sensing and image inpainting

Advances in Difference Equations

article

Suantai, Suthep¹  Noor, Muhammad Aslam³  Kankam, Kunrada⁴  Cholamjiak, Prasit⁴ 

[1] Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University;Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University;Department of Mathematics, COMSATS University Islamabad;School of Science, University of Phayao

关键词: Forward–backward algorithm;    Compressive sensing;    Image inpainting;    Minimization problem;   

DOI  :  10.1186/s13662-021-03422-9

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

The forward–backward algorithm is a splitting method for solving convex minimization problems of the sum of two objective functions. It has a great attention in optimization due to its broad application to many disciplines, such as image and signal processing, optimal control, regression, and classification problems. In this work, we aim to introduce new forward–backward algorithms for solving both unconstrained and constrained convex minimization problems by using linesearch technique. We discuss the convergence under mild conditions that do not depend on the Lipschitz continuity assumption of the gradient. Finally, we provide some applications to solving compressive sensing and image inpainting problems. Numerical results show that the proposed algorithm is more efficient than some algorithms in the literature. We also discuss the optimal choice of parameters in algorithms via numerical experiments.

【 授权许可】

CC BY