scholarly journals An Adaptive Image Denoising Model Based on Tikhonov and TV Regularizations

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Kui Liu ◽  
Jieqing Tan ◽  
Benyue Su
Keyword(s):  
Image Denoising ◽  
Total Variation ◽  
Tikhonov Regularization ◽  
Experimental Results ◽  
Total Variation Regularization ◽  
Split Bregman Method ◽  
Split Bregman ◽  
Gradient Information ◽  
Weighted Combination ◽  
Staircase Artifacts

To avoid the staircase artifacts, an adaptive image denoising model is proposed by the weighted combination of Tikhonov regularization and total variation regularization. In our model, Tikhonov regularization and total variation regularization can be adaptively selected based on the gradient information of the image. When the pixels belong to the smooth regions, Tikhonov regularization is adopted, which can eliminate the staircase artifacts. When the pixels locate at the edges, total variation regularization is selected, which can preserve the edges. We employ the split Bregman method to solve our model. Experimental results demonstrate that our model can obtain better performance than those of other models.

scholarly journals An efficient algorithm for adaptive total variation based image decomposition and restoration

2014 ◽  
Vol 24 (2) ◽  
pp. 405-415 ◽  
Author(s):  
Xinwu Liu ◽  
Lihong Huang
Keyword(s):  
Total Variation ◽  
Image Decomposition ◽  
Energy Functional ◽  
Total Variation Regularization ◽  
Split Bregman Method ◽  
Split Bregman ◽  
Edge Preserving ◽  
Sharp Edges ◽  
Adaptive Total Variation ◽  
Important Structure

Abstract With the aim to better preserve sharp edges and important structure features in the recovered image, this article researches an improved adaptive total variation regularization and H−1 norm fidelity based strategy for image decomposition and restoration. Computationally, for minimizing the proposed energy functional, we investigate an efficient numerical algorithm—the split Bregman method, and briefly prove its convergence. In addition, comparisons are also made with the classical OSV (Osher–Sole–Vese) model (Osher et al., 2003) and the TV-Gabor model (Aujol et al., 2006), in terms of the edge-preserving capability and the recovered results. Numerical experiments markedly demonstrate that our novel scheme yields significantly better outcomes in image decomposition and denoising than the existing models.

Total variation regularization for bioluminescence tomography with the split Bregman method

2012 ◽  
Vol 51 (19) ◽  
pp. 4501 ◽  
Author(s):  
Jinchao Feng ◽  
Chenghu Qin ◽  
Kebin Jia ◽  
Shouping Zhu ◽  
Kai Liu ◽  
...  
Keyword(s):  
Total Variation ◽  
Total Variation Regularization ◽  
Split Bregman Method ◽  
Split Bregman ◽  
Bioluminescence Tomography

Nonlocal Total Variation Based Image Deblurring Using Split Bregman Method and Fixed Point Iteration

2013 ◽  
Vol 333-335 ◽  
pp. 875-882 ◽  
Author(s):  
Dong Jie Tan ◽  
An Zhang
Keyword(s):  
Fixed Point ◽  
Total Variation ◽  
Image Deblurring ◽  
Benchmark Problems ◽  
Total Variation Regularization ◽  
Split Bregman Method ◽  
Split Bregman ◽  
Fixed Point Iteration ◽  
Nonlocal Total Variation ◽  
Nonlocal Regularization

Nonlocal regularization for image restoration is extensively studied in recent years. However, minimizing a nonlocal regularization problem is far more difficult than a local one and still challenging. In this paper, a novel nonlocal total variation based algorithm for image deblurring is presented. The core idea of this algorithm is to consider the latent image as the fixed point of the nonlocal total variation regularization functional. And a split Bregman method is proposed to solve the minimization problem in each fixed point iteration efficiently. By alternatively reconstructing a sharp image and updating the nonlocal gradient weights, the recovered image becomes more and more sharp. Experimental results on the benchmark problems are presented to show the efficiency and effectiveness of our algorithm.

scholarly journals Fast Algorithms for the Anisotropic LLT Model in Image Denoising

2011 ◽  
Vol 1 (3) ◽  
pp. 264-283 ◽  
Author(s):  
Zhi-Feng Pang ◽  
Li-Lian Wang ◽  
Yu-Fei Yang
Keyword(s):  
Convergence Rate ◽  
Image Denoising ◽  
Projection Method ◽  
Split Bregman Method ◽  
Split Bregman ◽  
Minimization Problems ◽  
Iterative Shrinkage ◽  
Speed Up ◽  
Thresholding Algorithm ◽  
Iterative Shrinkage Thresholding

AbstractIn this paper, we propose a new projection method for solving a general minimization problems with twoL1-regularization terms for image denoising. It is related to the split Bregman method, but it avoids solving PDEs in the iteration. We employ the fast iterative shrinkage-thresholding algorithm (FISTA) to speed up the proposed method to a convergence rateO(k−2). We also show the convergence of the algorithms. Finally, we apply the methods to the anisotropic Lysaker, Lundervold and Tai (LLT) model and demonstrate their efficiency.

scholarly journals Performance of relaxed iterative methods for image deblurring problems

2019 ◽  
Vol 13 ◽  
pp. 174830261986173 ◽  
Author(s):  
Jae H Yun
Keyword(s):  
Fixed Point ◽  
Iterative Methods ◽  
Total Variation ◽  
Numerical Experiments ◽  
Krylov Subspace ◽  
Image Deblurring ◽  
Total Variation Regularization ◽  
L1 Norm ◽  
Split Bregman ◽  
Relaxation Parameters

In this paper, we consider performance of relaxation iterative methods for four types of image deblurring problems with different regularization terms. We first study how to apply relaxation iterative methods efficiently to the Tikhonov regularization problems, and then we propose how to find good preconditioners and near optimal relaxation parameters which are essential factors for fast convergence rate and computational efficiency of relaxation iterative methods. We next study efficient applications of relaxation iterative methods to Split Bregman method and the fixed point method for solving the L1-norm or total variation regularization problems. Lastly, we provide numerical experiments for four types of image deblurring problems to evaluate the efficiency of relaxation iterative methods by comparing their performances with those of Krylov subspace iterative methods. Numerical experiments show that the proposed techniques for finding preconditioners and near optimal relaxation parameters of relaxation iterative methods work well for image deblurring problems. For the L1-norm and total variation regularization problems, Split Bregman and fixed point methods using relaxation iterative methods perform quite well in terms of both peak signal to noise ratio values and execution time as compared with those using Krylov subspace methods.

Four-directional fractional-order total variation regularization for image denoising

2017 ◽  
Vol 26 (05) ◽  
pp. 1 ◽  
Author(s):  
Linna Wu ◽  
Yingpin Chen ◽  
Jiaquan Jin ◽  
Hongwei Du ◽  
Bensheng Qiu
Keyword(s):  
Image Denoising ◽  
Total Variation ◽  
Fractional Order ◽  
Total Variation Regularization

Split Bregman method for the modified lot model in image denoising

2011 ◽  
Vol 217 (12) ◽  
pp. 5392-5403 ◽  
Author(s):  
Yu-Fei Yang ◽  
Zhi-Feng Pang ◽  
Bao-Li Shi ◽  
Zhi-Guo Wang
Keyword(s):  
Image Denoising ◽  
Split Bregman Method ◽  
Split Bregman
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