A High-Order Model of TV and its Augmented Lagrangian Algorithm

2014 ◽  
Vol 568-570 ◽  
pp. 726-733 ◽  
Author(s):  
Lu Tan ◽  
Wei Bo Wei ◽  
Zhen Kuan Pan ◽  
Wei Zhong Zhang ◽  
Jin Ming Duan
Keyword(s):  
Image Denoising ◽  
High Order ◽  
Order Model ◽  
Split Bregman ◽  
Denoising Method ◽  
Proposed Model ◽  
Total Variation Model ◽  
Staircase Effect ◽  
Variational Image ◽  
Split Bregman Algorithm

In recent twenty years, image denoising method which is based on partial differential equations (PDE) has been developed rapidly. Due to its scientific and strong theoretical foundation, it owns accurate and stable results which can be got by efficient algorithms. But it still leaves some problems which need to be solved. The staircase effect is one of the most basic problems in the classical TV (Total Variation) model. This problem can be effectively solved by high-order model proposed in this paper. A fast and efficient numerical algorithm is designed to solve minimization problems related to the high-order model and its applications to variational image denoising are shown. The performance of the proposed model is compared with TV model and other high-order models. The algorithm used for the proposed model is also compared with Split Bregman algorithm. Some numerical experiments validate the model proposed and the algorithm designed in this paper.

scholarly journals A Novel Health Prognosis Method for a Power System Based on a High-Order Hidden Semi-Markov Model

Energies ◽  
2021 ◽  
Vol 14 (24) ◽  
pp. 8208
Author(s):  
Qinming Liu ◽  
Daigao Li ◽  
Wenyi Liu ◽  
Tangbin Xia ◽  
Jiaxiang Li
Keyword(s):  
Power System ◽  
Markov Model ◽  
Optimization Algorithm ◽  
High Order ◽  
Residual Lifetime ◽  
Health State ◽  
Order Model ◽  
Intelligent Optimization ◽  
Proposed Model ◽  
Intelligent Optimization Algorithm

Power system health prognosis is a key process of condition-based maintenance. For the problem of large error in the residual lifetime prognosis of a power system, a novel residual lifetime prognosis model based on a high-order hidden semi-Markov model (HOHSMM) is proposed. First, HOHSMM is developed based on the hidden semi-Markov model (HSMM). An order reduction method and a composite node mechanism of HOHSMM based on permutation are proposed. The health state transition matrix and observation matrix are improved accordingly. The high-order model is transformed into the corresponding first-order model, and more node dependency information is stored in the parameter group to be estimated. Secondly, in order to estimate the parameters and optimize the structure of the proposed model, an intelligent optimization algorithm group is used instead of the expectation–maximization (EM) algorithm. Thus, the simplification of the topology of the high-order model by the intelligent optimization algorithm can be realized. Then, the state duration variables in the high-order model are defined and deduced. The prognosis method based on polynomial fitting is used to predict the residual lifetime of the power system when the prior distribution is unknown. Finally, the intelligent optimization algorithm is used to solve the proposed model, and experiments are performed based on a set of power system data sets to evaluate the performance of the proposed model. Compared with HSMM, the proposed model has better performance on the power system health prognosis problem and can get a relatively good solution in a short computation time.

scholarly journals Local and Nonlocal Steering Kernel Weighted Total Variation Model for Image Denoising

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 329 ◽  
Author(s):  
Rui Lai ◽  
Yiguo Mo ◽  
Zesheng Liu ◽  
Juntao Guan
Keyword(s):  
Image Denoising ◽  
Total Variation ◽  
Noise Suppression ◽  
Nonlocal Symmetry ◽  
Visual Appearance ◽  
Quantitative Indices ◽  
Proposed Model ◽  
Total Variation Model ◽  
Weighted Total Variation ◽  
Tv Model

To eliminate heavy noise and retain more scene details, we propose a structure-oriented total variation (TV) model based on data dependent kernel function and TV criterion for image denoising application. The innovative model introduces the weights produced from the local and nonlocal symmetry features involved in the image itself to pick more precise solutions in the TV denoising process. As a result, the proposed local and nonlocal steering kernel weighted TV model yields excellent noise suppression and structure-preserving performance. The experimental results verify the validity of the proposed model in objective quantitative indices and subjective visual appearance.

scholarly journals Research on the Image Denoising Method Based on Partial Differential Equations

2016 ◽  
Vol 16 (5) ◽  
pp. 109-118
Author(s):  
Xiaolu Xie
Keyword(s):  
Image Denoising ◽  
High Performance ◽  
Signal To Noise Ratio ◽  
Similarity Index ◽  
Structural Similarity ◽  
Structural Similarity Index ◽  
Denoising Method ◽  
New Approach ◽  
Proposed Model ◽  
Index Measure

Abstract In this paper we propose a new approach for image denoising based on the combination of PM model, isotropic diffusion model, and TV model. To emphasize the superiority of the proposed model, we have used the Structural Similarity Index Measure (SSIM) and Peak Signal to Noise Ratio (PSNR) as the subjective criterion. Numerical experiments with different images show that our algorithm has the highest PSNR and SS1M, as well as the best visual quality among the six algorithms. Experimental results confirm the high performance of the proposed model compared with some well-known algorithms. In a word, the new model outperforms the mentioned three well known algorithms in reducing the Gibbs-type artifacts, edges blurring, and the block effect, simultaneously.

scholarly journals AN ADAPTIVE VARIATIONAL MODEL FOR MEDICAL IMAGES RESTORATION

2019 ◽  
Vol XLII-2/W12 ◽  
pp. 219-224
Author(s):  
T. T. T. Tran ◽  
C. T. Pham ◽  
A. V. Kopylov ◽  
V. N. Nguyen
Keyword(s):  
Optimization Problem ◽  
Medical Images ◽  
Variational Model ◽  
Imaging Analysis ◽  
Split Bregman Method ◽  
Split Bregman ◽  
Piecewise Constant ◽  
First Order ◽  
Proposed Model ◽  
Staircase Effect

<p><strong>Abstract.</strong> Image denoising is one of the important tasks required by medical imaging analysis. In this work, we investigate an adaptive variation model for medical images restoration. In the proposed model, we have used the first-order total variation combined with Laplacian regularizer to eliminate the staircase effect in the first-order TV model while preserve edges of object in the piecewise constant image. We also propose an instance of Split Bregman method to solve the proposed denoising model as an optimization problem. Experimental results from mixed Poisson-Gaussian noise are given to demonstrate that our proposed approach outperforms the related methods.</p>

scholarly journals High-Order Total Bounded Variation Model and Its Fast Algorithm for Poissonian Image Restoration

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Jun Zhang ◽  
Mingxi Ma ◽  
Zhaoming Wu ◽  
Chengzhi Deng
Keyword(s):  
Image Restoration ◽  
Bounded Variation ◽  
Optimal Solution ◽  
High Order ◽  
Convergence Theory ◽  
Convex Model ◽  
Split Bregman ◽  
Strongly Convex ◽  
Global Optimal ◽  
Split Bregman Algorithm

In this paper, a new model for image restoration under Poisson noise based on a high-order total bounded variation is proposed. Existence and uniqueness of its solution are proved. To find the global optimal solution of our strongly convex model, a split Bregman algorithm is introduced. Furthermore, a rigorous convergence theory of the proposed algorithm is established. Experimental results are provided to demonstrate the effectiveness and efficiency of the proposed method over the classic total bounded variation-based model.

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.

An image Denoising Method Based On Multi Resulation Bilateral Filter

2018 ◽  
Vol 6 (12) ◽  
pp. 448-452
Author(s):  
Md Shaiful Islam Babu ◽  
Kh Shaikh Ahmed ◽  
Md Samrat Ali Abu Kawser ◽  
Ajkia Zaman Juthi
Keyword(s):  
Image Denoising ◽  
Bilateral Filter ◽  
Denoising Method
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