Dual algorithm for truncated fractional variation based image denoising

Liang, HX;Zhang, JL

[Liang, Haixia] Xian Jiaotong Liverpool Univ, Dept Math Sci, 111 Renai Rd,Suzhou Ind Pk, Suzhou, Jiangsu, Peoples R China.
[Zhang, Juli] Shanghai Univ Engn Sci, Sch Math Phys & Stat, Shanghai, Peoples R China.

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS

Volume:97 Issue:9Pages:1849-1859

DOI:10.1080/00207160.2019.1664737

Publication Year:2020

JCR:Q2

CAS JCR:3区

ESI Discipline:ENGINEERING

Latest Impact Factor:1.931

Document Type:Journal Article

Identifier:http://hdl.handle.net/20.500.12791/002518

Abstract

Fractional-order derivative is attracting more and more attention of researchers in image processing because of its better property in restoring more texture than the total variation. To improve the performance of fractional-order variation model in image restoration, a truncated fractional-order variation model was proposed in Chan and Liang [Truncated fractional-order variation model for image restoration, J. Oper. Res. Soc. China]. In this paper, we propose a dual approach to solve this truncated fractional-order variation model on noise removal. The proposed algorithm is based on the dual approach proposed by Chambolle [An algorithm for total variation minimisation and applications, J. Math Imaging Vis. 20 (2004), pp. 89-97]. Conversely, the Chambolle's dual approach can be treated as a special case of the proposed algorithm with fractional order . The work of this paper modifies the result in Zhang et al. [Adaptive fractional-order multi-scale method for image denoising, J. Math. Imaging Vis. 43(1) (2012), pp. 39-49. Springer Netherlands 0924-9907, Computer Science, pp. 1-11, 2011], where the convergence is not analysed. Based on the truncation, the convergence of the proposed dual method can be analysed and the convergence criteria can be provided. In addition, the accuracy of the reconstruction is improved after the truncation is taken.

Keywords

dual algorithm truncated fractional-order variation model texture preserving Truncated fractional-order derivative image denoising

Copyright 2006-2020 © Xi'an Jiaotong-Liverpool University 苏ICP备07016150号-1 京公网安备 11010102002019号