scholarly journals Fast Total-Variation Image Deconvolution with Adaptive Parameter Estimation via Split Bregman Method

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Chuan He ◽  
Changhua Hu ◽  
Wei Zhang ◽  
Biao Shi ◽  
Xiaoxiang Hu
Keyword(s):  
Total Variation ◽  
Regularization Parameter ◽  
Difficult Problem ◽  
Image Deconvolution ◽  
Split Bregman Method ◽  
Split Bregman ◽  
Edge Preservation ◽  
Adaptive Parameter ◽  
Tv Regularization ◽  
Blurred Image

The total-variation (TV) regularization has been widely used in image restoration domain, due to its attractive edge preservation ability. However, the estimation of the regularization parameter, which balances the TV regularization term and the data-fidelity term, is a difficult problem. In this paper, based on the classical split Bregman method, a new fast algorithm is derived to simultaneously estimate the regularization parameter and to restore the blurred image. In each iteration, the regularization parameter is refreshed conveniently in a closed form according to Morozov’s discrepancy principle. Numerical experiments in image deconvolution show that the proposed algorithm outperforms some state-of-the-art methods both in accuracy and in speed.

scholarly journals Efficient Algorithm for Isotropic and Anisotropic Total Variation Deblurring and Denoising

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Yuying Shi ◽  
Qianshun Chang
Keyword(s):  
Nonlinear System ◽  
Total Variation ◽  
Multigrid Method ◽  
Algebraic Multigrid ◽  
Split Bregman Method ◽  
Split Bregman ◽  
Linearized System ◽  
Outer Iteration ◽  
Anisotropic Total Variation ◽  
Deblurring And Denoising

A new deblurring and denoising algorithm is proposed, for isotropic total variation-based image restoration. The algorithm consists of an efficient solver for the nonlinear system and an acceleration strategy for the outer iteration. For the nonlinear system, the split Bregman method is used to convert it into linear system, and an algebraic multigrid method is applied to solve the linearized system. For the outer iteration, we have conducted formal convergence analysis to determine an auxiliary linear term that significantly stabilizes and accelerates the outer iteration. Numerical experiments demonstrate that our algorithm for deblurring and denoising problems is efficient.

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 Improved Total Variation Minimization Method Using Prior Images and Split-Bregman Method in CT Reconstruction

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Luzhen Deng ◽  
Peng Feng ◽  
Mianyi Chen ◽  
Peng He ◽  
Biao Wei
Keyword(s):  
Total Variation ◽  
Locally Linear Embedding ◽  
Projection Data ◽  
Reconstruction Method ◽  
Ct Reconstruction ◽  
Split Bregman Method ◽  
Split Bregman ◽  
Minimization Method ◽  
Total Variation Minimization ◽  
Image Objects

Compressive Sensing (CS) theory has great potential for reconstructing Computed Tomography (CT) images from sparse-views projection data and Total Variation- (TV-) based CT reconstruction method is very popular. However, it does not directly incorporate prior images into the reconstruction. To improve the quality of reconstructed images, this paper proposed an improved TV minimization method using prior images and Split-Bregman method in CT reconstruction, which uses prior images to obtain valuable previous information and promote the subsequent imaging process. The images obtained asynchronously were registered via Locally Linear Embedding (LLE). To validate the method, two studies were performed. Numerical simulation using an abdomen phantom has been used to demonstrate that the proposed method enables accurate reconstruction of image objects under sparse projection data. A real dataset was used to further validate the method.

Total variation regularization for depth-to-basement estimate: Part 2 — Physicogeologic meaning and comparisons with previous inversion methods

Geophysics ◽  
2011 ◽  
Vol 76 (1) ◽  
pp. I13-I20 ◽  
Author(s):  
Williams A. Lima ◽  
Cristiano M. Martins ◽  
João B. Silva ◽  
Valeria C. Barbosa
Keyword(s):  
Total Variation ◽  
Regularization Parameter ◽  
Synthetic Data ◽  
Gravity Inversion ◽  
Total Variation Regularization ◽  
Discontinuous Solutions ◽  
Mathematical Basis ◽  
Inversion Methods ◽  
Tv Regularization ◽  
Entropic Regularization

We applied the mathematical basis of the total variation (TV) regularization to analyze the physicogeologic meaning of the TV method and compared it with previous gravity inversion methods (weighted smoothness and entropic Regularization) to estimate discontinuous basements. In the second part, we analyze the physicogeologic meaning of the TV method and compare it with previous gravity inversion methods (weighted smoothness and entropic regularization) to estimate discontinuous basements. Presenting a mathematical review of these methods, we show that minimizing the TV stabilizing function favors discontinuous solutions because a smooth solution, to honor the data, must oscillate, and the presence of these oscillations increases the value of the TV stabilizing function. These three methods are applied to synthetic data produced by a simulated 2D graben bordered by step faults. TV regularization and weighted smoothness are also applied to the real anomaly of Steptoe Valley, Nevada, U.S.A. In all applications, the three methods perform similarly. TV regularization, however, has the advantage, compared with weighted smoothness, of requiring no a priori information about the maximum depth of the basin. As compared with entropic regularization, TV regularization is much simpler to use because it requires, in general, the tuning of just one regularization parameter.

Adaptive total variation-based spectral deconvolution with the split Bregman method

2014 ◽  
Vol 53 (35) ◽  
pp. 8240 ◽  
Author(s):  
Hai Liu ◽  
Sanya Liu ◽  
Zhaoli Zhang ◽  
Jianwen Sun ◽  
Jiangbo Shu
Keyword(s):  
Total Variation ◽  
Split Bregman Method ◽  
Split Bregman ◽  
Spectral Deconvolution ◽  
Adaptive Total Variation
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