A new difference of anisotropic and isotropic total variation regularization method for image restoration

Benxin Zhang; Xiaolong Wang; Yi Li; Zhibin Zhu; Benxin Zhang; Xiaolong Wang; Yi Li; Zhibin Zhu

doi:10.3934/mbe.2023661

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 8: 14777-14792. doi: 10.3934/mbe.2023661

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Research article

A new difference of anisotropic and isotropic total variation regularization method for image restoration

1.
School of Electronic Engineering and Automation, Guilin University of Electronic Technology, Guilin 541004, China
2.
School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, China

Received: 07 May 2023 Revised: 18 June 2023 Accepted: 27 June 2023 Published: 07 July 2023

Total variation (TV) regularizer has diffusely emerged in image processing. In this paper, we propose a new nonconvex total variation regularization method based on the generalized Fischer-Burmeister function for image restoration. Since our model is nonconvex and nonsmooth, the specific difference of convex algorithms (DCA) are presented, in which the subproblem can be minimized by the alternating direction method of multipliers (ADMM). The algorithms have a low computational complexity in each iteration. Experiment results including image denoising and magnetic resonance imaging demonstrate that the proposed models produce more preferable results compared with state-of-the-art methods.
- image restoration,
- TV,
- Fischer-Burmeister function,
- DCA,
- ADMM
Citation: Benxin Zhang, Xiaolong Wang, Yi Li, Zhibin Zhu. A new difference of anisotropic and isotropic total variation regularization method for image restoration[J]. Mathematical Biosciences and Engineering, 2023, 20(8): 14777-14792. doi: 10.3934/mbe.2023661

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Abstract

Total variation (TV) regularizer has diffusely emerged in image processing. In this paper, we propose a new nonconvex total variation regularization method based on the generalized Fischer-Burmeister function for image restoration. Since our model is nonconvex and nonsmooth, the specific difference of convex algorithms (DCA) are presented, in which the subproblem can be minimized by the alternating direction method of multipliers (ADMM). The algorithms have a low computational complexity in each iteration. Experiment results including image denoising and magnetic resonance imaging demonstrate that the proposed models produce more preferable results compared with state-of-the-art methods.

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