scholarly journals Multiplicative Noise Removal Based on the Linear Alternating Direction Method for a Hybrid Variational Model

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Yan Hao ◽  
Jianlou Xu ◽  
Fengyun Zhang ◽  
Xiaobo Zhang
Keyword(s):  
Total Variation ◽  
Multiplicative Noise ◽  
Splitting Method ◽  
Noise Removal ◽  
Variational Model ◽  
Total Variation Regularization ◽  
Alternating Direction ◽  
Staircase Effect ◽  
Multiplicative Noise Removal ◽  
Alternative Direction Method

To preserve the edge, multiplicative noise removal models based on the total variation regularization have been widely studied, but they suffer from the staircase effect. In this paper, to preserve the edge and reduce the staircase effect, we develop a hybrid variational model based on the variable splitting method for multiplicative noise removal; the new model is a strictly convex objective function which contains the total variation regularization and a modified regularization term. We use the linear alternative direction method to find the minimal solution and also give the convergence proof of the proposed algorithm. Experimental results verify that the proposed model can obtain the better results for removing the multiplicative noise compared with the recent method.

scholarly journals A Fast High-Order Total Variation Minimization Method for Multiplicative Noise Removal

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Xiao-Guang Lv ◽  
Jiang Le ◽  
Jin Huang ◽  
Liu Jun
Keyword(s):  
Total Variation ◽  
Multiplicative Noise ◽  
Noise Removal ◽  
High Order ◽  
Alternating Minimization ◽  
Minimization Method ◽  
Total Variation Minimization ◽  
Alternating Minimization Algorithm ◽  
Staircase Effect ◽  
Multiplicative Noise Removal

Multiplicative noise removal problem has received considerable attention in recent years. The total variation regularization method for the solution of the noise removal problem can preserve edges well but has the sometimes undesirable staircase effect. In this paper, we propose a fast high-order total variation minimization method to restore multiplicative noisy images. The proposed method is able to preserve edges and at the same time avoid the staircase effect in the smooth regions. An alternating minimization algorithm is employed to solve the proposed high-order total variation minimization problem. We discuss the convergence of the alternating minimization algorithm. Some numerical results show that the proposed method gives restored images of higher quality than some existing multiplicative noise removal methods.

scholarly journals Image Restoration by a Mixed High-Order Total Variation and l1 Regularization Model

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Jianguang Zhu ◽  
Kai Li ◽  
Binbin Hao
Keyword(s):  
Total Variation ◽  
High Order ◽  
Variational Model ◽  
Total Variation Regularization ◽  
Current State ◽  
Model Combining ◽  
Alternating Direction ◽  
Proposed Model ◽  
Sharp Edges ◽  
Thresholding Algorithm

Total variation regularization is well-known for recovering sharp edges; however, it usually produces staircase artifacts. In this paper, in order to overcome the shortcoming of total variation regularization, we propose a new variational model combining high-order total variation regularization and l1 regularization. The new model has separable structure which enables us to solve the involved subproblems more efficiently. We propose a fast alternating method by employing the fast iterative shrinkage-thresholding algorithm (FISTA) and the alternating direction method of multipliers (ADMM). Compared with some current state-of-the-art methods, numerical experiments show that our proposed model can significantly improve the quality of restored images and obtain higher SNR and SSIM values.

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