A Projected Forward-Backward Algorithm for Constrained Minimization with Applications to Image Inpainting

Mathematics

Suthep Suantai¹  Prasit Cholamjiak²  Kunrada Kankam² 

[1] Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand;School of Science, University of Phayao, Phayao 56000, Thailand;

关键词: convex minimization;    image inpainting;    inertial techniques;    weak convergence;   

DOI  :  10.3390/math9080890

来源: DOAJ

【 摘 要 】

In this research, we study the convex minimization problem in the form of the sum of two proper, lower-semicontinuous, and convex functions. We introduce a new projected forward-backward algorithm using linesearch and inertial techniques. We then establish a weak convergence theorem under mild conditions. It is known that image processing such as inpainting problems can be modeled as the constrained minimization problem of the sum of convex functions. In this connection, we aim to apply the suggested method for solving image inpainting. We also give some comparisons to other methods in the literature. It is shown that the proposed algorithm outperforms others in terms of iterations. Finally, we give an analysis on parameters that are assumed in our hypothesis.

【 授权许可】

Unknown