Performance of the Restarted Homotopy Perturbation Method and Split Bregman Method for Multiplicative Noise Removal. (6th December 2018)

• Record Type: Journal Article
• Authors: Han, Yu Du; Yun, Jae Heon
• Other Names: Schuster Thomas Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2018(2018)
• Publication Date: 2018-12-06
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2018/7696798
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : In this paper, we first propose restarted homotopy perturbation methods (RHPM) for multiplicative noise removal of the RLO and AA2 models. The main difficulty in applying the RHPM to the nonlinear denoising problem is settled by using binomial series techniques. We next propose the split Bregman methods for multiplicative noise removal of the RLO and AA2 models. The difficulty in applying the split Bregman method to the nonlinear denoising problem can be handled by transforming ill-conditioned linear systems into well-conditioned linear systems using splitting techniques of singular matrices. Lastly, numerical experiments for several test problems are provided to demonstrate the efficiency and reliability of the RHPM and split Bregman methods.