Proximal alternating minimization method for adaptive TGV-based image restoration
- PDF / 1,604,179 Bytes
- 14 Pages / 439.642 x 666.49 pts Page_size
- 95 Downloads / 199 Views
Proximal alternating minimization method for adaptive TGV-based image restoration Xinwu Liu1 Received: 1 January 2020 / Revised: 1 August 2020 / Accepted: 6 August 2020 / © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract This article presents an adaptive total generalized variation regularized strategy for image reconstruction. Unlike the traditional fixed weights schemes, our weights can be adaptively updated according to the latest computations. This helps to obtain more accurate numerical solutions and avoid the troublesome parameters selection. Subsequently, by artfully employing the Moreau decomposition and proximal algorithm, we develop a highly efficient proximal alternating minimization method to optimize the objective function in detail. The introduced technique has the capability of automatically estimating the regularization parameter and restoring the deteriorated image. Finally, several numerical simulations concertedly illustrate the competitive superiority of our proposed scheme for image restoration, especially in terms of suppressing staircase artifacts and maintaining edge details. Keywords Image restoration · Additive noise · Adaptive total generalized variation · Proximal operator · Alternating minimization method
1 Introduction Image restoration, which aims to recover the unknown clean image u from its degradation f , is a significant and challenging inverse problem in imaging science. As a further application, it can be widely applied in high-level image processing, such as feature recognition [2, 23], medical image [12, 31], and image encryption [41]. Mathematically speaking, the commonly used model can be defined as f = Ku + η, where K is a linear operator denoting the blur, and η represents the additive Gaussian noise. The problem of reconstructing u from the above model is ill-posed. Therefore, to deal with the ill-posedness, an efficient technique is to add a regularization term to the energy based on the maximum likelihood principle. This work was supported by National Natural Science Foundation of China (61402166), Scientific Research Fund of Hunan Provincial Education Department (19B215) and Hunan Provincial Natural Science Foundation of China (2020JJ4285). Xinwu Liu
[email protected] 1
School of Mathematics and Computational Science, Hunan University of Science and Technology, Xiangtan 411201, Hunan, China
Multimedia Tools and Applications
Among them, one remarkable example is the total variation (TV) regularized variational model, which was originally introduced by Rudin et al. [34]. The optimization model can be written as λ (1) min TV(u) + Ku − f 22 , u 2 where the function TV(u) is a regularization, the second term measures the fidelity of data, and λ indicates a positive weighting constant. In various applications, such as image fusion [16, 22, 29, 43] and hyperspectral image denoising [11], numerical results demonstrate the effectiveness of the TV-based solvers for preserving edge details and structural features. Unfortunately, the above TV fr
Data Loading...
