Anisotropic Total Variation Guided Filtering and Its Split Bregman Algorithm

2017 ◽  
Vol 54 (5) ◽  
pp. 051005
Author(s):  
芦碧波 Lu Bibo ◽  
王乐蓉 Wang Lerong ◽  
王永茂 Wang Yongmao ◽  
郑艳梅 Zheng Yanmei
Keyword(s):  
Total Variation ◽  
Split Bregman ◽  
Guided Filtering ◽  
Split Bregman Algorithm ◽  
Anisotropic Total Variation

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.

Data-driven multichannel seismic impedance inversion with anisotropic total variation regularization

2018 ◽  
Vol 26 (2) ◽  
pp. 229-241 ◽  
Author(s):  
Dehua Wang ◽  
Jinghuai Gao ◽  
Hongan Zhou
Keyword(s):  
Total Variation ◽  
Seismic Data ◽  
Reservoir Characterization ◽  
Data Driven ◽  
Total Variation Regularization ◽  
Split Bregman ◽  
Seismic Reflection Data ◽  
Reflection Data ◽  
Impedance Inversion ◽  
Anisotropic Total Variation

AbstractAcoustic impedance (AI) inversion is a desirable tool to extract rock-physical properties from recorded seismic data. It plays an important role in seismic interpretation and reservoir characterization. When one of recursive inversion schemes is employed to obtain the AI, the spatial coherency of the estimated reflectivity section may be damaged through the trace-by-trace processing. Meanwhile, the results are sensitive to noise in the data or inaccuracies in the generated reflectivity function. To overcome the above disadvantages, in this paper, we propose a data-driven inversion scheme to directly invert the AI from seismic reflection data. We first explain in principle that the anisotropic total variation (ATV) regularization is more suitable for inverting the impedance with sharp interfaces than the total variation (TV) regularization, and then establish the nonlinear objective function of the AI model by using anisotropic total variation (ATV) regularization. Next, we solve the nonlinear impedance inversion problem via the alternating split Bregman iterative algorithm. Finally, we illustrate the performance of the proposed method and its robustness to noise with synthetic and real seismic data examples by comparing with the conventional methods.

scholarly journals SIMRES-TV: NOISE AND RESIDUAL SIMILARITY FOR PARAMETER ESTIMATION IN TOTAL VARIATION

2021 ◽  
Vol XLIV-2/W1-2021 ◽  
pp. 171-176
Author(s):  
V. B. S. Prasath ◽  
N. N. Hien ◽  
D. N. H. Thanh ◽  
S. Dvoenko
Keyword(s):  
Image Processing ◽  
Parameter Estimation ◽  
Image Restoration ◽  
Total Variation ◽  
Regularization Parameter ◽  
Noise Levels ◽  
Split Bregman ◽  
Edge Preserving ◽  
Restoration Scheme ◽  
Split Bregman Algorithm

Abstract. Image restoration with regularization models is very popular in the image processing literature. Total variation (TV) is one of the important edge preserving regularization models used, however, to obtain optimal restoration results the regularization parameter needs to be set appropriately. We propose here a new parameter estimation approach for total variation based image restoration. By utilizing known noise levels we compute the regularization parameter by reducing the similarity between residual and noise variances. We use the split Bregman algorithm for the total variation along with this automatic parameter estimation step to obtain a very fast restoration scheme. Experimental results indicate the proposed parameter estimation obtained better denoised images and videos in terms of PSNR and SSIM measures and the computational overload is less compared with other approaches.

An Efficient Proximity Point Algorithm for Total-Variation-Based Image Restoration

2014 ◽  
Vol 6 (2) ◽  
pp. 145-164 ◽  
Author(s):  
Wei Zhu ◽  
Shi Shu ◽  
Lizhi Cheng
Keyword(s):  
Image Restoration ◽  
Total Variation ◽  
Projection Algorithm ◽  
Split Bregman ◽  
Fixed Point Algorithm ◽  
First Order ◽  
Special Cases ◽  
Point Operator ◽  
Novel Method ◽  
Split Bregman Algorithm

AbstractIn this paper, we propose a fast proximity point algorithm and apply it to total variation (TV) based image restoration. The novel method is derived from the idea of establishing a general proximity point operator framework based on which new first-order schemes for total variation (TV) based image restoration have been proposed. Many current algorithms for TV-based image restoration, such as Chambolle’s projection algorithm, the split Bregman algorithm, the Bermúdez-Moreno algorithm, the Jia-Zhao denoising algorithm, and the fixed point algorithm, can be viewed as special cases of the new first-order schemes. Moreover, the convergence of the new algorithm has been analyzed at length. Finally, we make comparisons with the split Bregman algorithm which is one of the best algorithms for solving TV-based image restoration at present. Numerical experiments illustrate the efficiency of the proposed algorithms.

scholarly journals An algorithm combining coordinate descent and split Bregman iterative for fractional image denoising model

2021 ◽  
Vol 15 ◽  
pp. 174830262110311
Author(s):  
Donghong Zhao ◽  
Yonghua Fan ◽  
Haoyu Liu ◽  
Yafeng Yang
Keyword(s):  
Total Variation ◽  
Minimization Problem ◽  
Optimization Problems ◽  
Descent Method ◽  
Coordinate Descent ◽  
Split Bregman ◽  
Coordinate Descent Method ◽  
Total Variation Model ◽  
Split Bregman Algorithm ◽  
Variation Model

The split Bregman algorithm and the coordinate descent method are efficient tools for solving optimization problems, which have been proven to be effective for the total variation model. We propose an algorithm for fractional total variation model in this paper, and employ the coordinate descent method to decompose the fractional-order minimization problem into scalar sub-problems, then solve the sub-problem by using split Bregman algorithm. Numerical results are presented in the end to demonstrate the superiority of the proposed algorithm.

Multiple Aerosol Unmixing by the Split Bregman Algorithm

2011 ◽  
Author(s):  
Russell Warren ◽  
Stanley Osher ◽  
Richard Vanderbeek
Keyword(s):  
Split Bregman ◽  
Split Bregman Algorithm

scholarly journals Fast Split Bregman Based Deconvolution Algorithm for Airborne Radar Imaging

2020 ◽  
Vol 12 (11) ◽  
pp. 1747 ◽  
Author(s):  
Yin Zhang ◽  
Qiping Zhang ◽  
Yongchao Zhang ◽  
Jifang Pei ◽  
Yulin Huang ◽  
...  
Keyword(s):  
Real Time ◽  
Computing Time ◽  
Real Data ◽  
Radar Imaging ◽  
Matrix Inversion ◽  
Airborne Radar ◽  
Split Bregman ◽  
Regularization Problem ◽  
Azimuth Resolution ◽  
Split Bregman Algorithm

Deconvolution methods can be used to improve the azimuth resolution in airborne radar imaging. Due to the sparsity of targets in airborne radar imaging, an L 1 regularization problem usually needs to be solved. Recently, the Split Bregman algorithm (SBA) has been widely used to solve L 1 regularization problems. However, due to the high computational complexity of matrix inversion, the efficiency of the traditional SBA is low, which seriously restricts its real-time performance in airborne radar imaging. To overcome this disadvantage, a fast split Bregman algorithm (FSBA) is proposed in this paper to achieve real-time imaging with an airborne radar. Firstly, under the regularization framework, the problem of azimuth resolution improvement can be converted into an L 1 regularization problem. Then, the L 1 regularization problem can be solved with the proposed FSBA. By utilizing the low displacement rank features of Toeplitz matrix, the proposed FSBA is able to realize fast matrix inversion by using a Gohberg–Semencul (GS) representation. Through simulated and real data processing experiments, we prove that the proposed FSBA significantly improves the resolution, compared with the Wiener filtering (WF), truncated singular value decomposition (TSVD), Tikhonov regularization (REGU), Richardson–Lucy (RL), iterative adaptive approach (IAA) algorithms. The computational advantage of FSBA increases with the increase of echo dimension. Its computational efficiency is 51 times and 77 times of the traditional SBA, respectively, for echoes with dimensions of 218 × 400 and 400 × 400 , optimizing both the image quality and computing time. In addition, for a specific hardware platform, the proposed FSBA can process echo of greater dimensions than traditional SBA. Furthermore, the proposed FSBA causes little performance degradation, when compared with the traditional SBA.

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