A fixed-point algorithm for second-order total variation models in image denoising

In this paper, we construct fixed-point algorithms for the second-order total variation models through discretization models and the subdifferential and proximity operators. Particularly, we focus on the convergence conditions of our algorithms by analyzing the eigenvalues of the difference matrix....

Full description

Saved in:
Bibliographic Details
Published inComputational & applied mathematics Vol. 38; no. 1; pp. 1 - 14
Main Authors Gao, Tianling, Wang, Xiaofei, Liu, Qiang, Zhang, Zhiguang
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.03.2019
Springer Nature B.V
Subjects
Algorithms
Applications of Mathematics
Applied physics
Computational mathematics
Computational Mathematics and Numerical Analysis
Convergence
Eigenvalues
Fixed points (mathematics)
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Noise reduction
68U10
65K10
Fixed-point algorithm
High-order total variation
Convergence
Image denoising
Online AccessGet full text

Cover

More Information
Summary:In this paper, we construct fixed-point algorithms for the second-order total variation models through discretization models and the subdifferential and proximity operators. Particularly, we focus on the convergence conditions of our algorithms by analyzing the eigenvalues of the difference matrix. The algorithms are tested on various images to verify our proposed convergence conditions. The experiments compared with the split Bregman algorithms demonstrate that fixed-point algorithms could solve the second-order functional minimization problem stably and effectively.
ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-019-0763-2