Total Variation Based Parameter-Free Model for Impulse Noise Removal

2017 ◽  
Vol 10 (1) ◽  
pp. 186-204 ◽  
Author(s):  
Federica Sciacchitano ◽  
Yiqiu Dong ◽  
Martin S. Andersen
Keyword(s):  
Total Variation ◽  
Impulse Noise ◽  
Regularization Parameter ◽  
Noise Removal ◽  
Phase Method ◽  
Second Phase ◽  
Dual Algorithm ◽  
Two Phase ◽  
Total Variation Minimization ◽  
Primal Dual

AbstractWe propose a new two-phase method for reconstruction of blurred images corrupted by impulse noise. In the first phase, we use a noise detector to identify the pixels that are contaminated by noise, and then, in the second phase, we reconstruct the noisy pixels by solving an equality constrained total variation minimization problem that preserves the exact values of the noise-free pixels. For images that are only corrupted by impulse noise (i.e., not blurred) we apply the semismooth Newton's method to a reduced problem, and if the images are also blurred, we solve the equality constrained reconstruction problem using a first-order primal-dual algorithm. The proposed model improves the computational efficiency (in the denoising case) and has the advantage of being regularization parameter-free. Our numerical results suggest that the method is competitive in terms of its restoration capabilities with respect to the other two-phase methods.

A simple primal-dual algorithm for nuclear norm and total variation regularization

2018 ◽  
Vol 289 ◽  
pp. 1-12 ◽  
Author(s):  
Zhibin Zhu ◽  
Jiawen Yao ◽  
Zheng Xu ◽  
Junzhou Huang ◽  
Benxin Zhang
Keyword(s):  
Total Variation ◽  
Nuclear Norm ◽  
Total Variation Regularization ◽  
Dual Algorithm ◽  
Primal Dual

scholarly journals Virtual interpolation of discrete multi-objective programming solutions with probabilistic operation

2011 ◽  
Vol 22 (4) ◽  
pp. 379-389
Author(s):  
Ricardo C. Silva ◽  
Edilson F. Arruda ◽  
Fabrício O. Ourique
Keyword(s):  
Probability Distributions ◽  
Phase Method ◽  
Second Phase ◽  
Pareto Optimal ◽  
Two Phase ◽  
Term Operation ◽  
Multi Objective ◽  
Multi Objective Programming ◽  
Objective Programming

This work presents a novel framework to address the long term operation of a class of multi-objective programming problems. The proposed approach considers a stochastic operation and evaluates the long term average operating costs/profits. To illustrate the approach, a two-phase method is proposed which solves a prescribed number of K mono-objective problems to identify a set of K points in the Pareto-optimal region. In the second phase, one searches for a set of non-dominated probability distributions that define the probability that the system operates at each point selected in the first phase, at any given operation period. Each probability distribution generates a vector of average long-term objectives and one solves for the Pareto-optimal set with respect to the average objectives. The proposed approach can generate virtual operating points with average objectives that need not have a feasible solution with an equal vector of objectives. A few numerical examples are presented to illustrate the proposed method.

Adaptive Weighted Generalized Total Variation Image Deblurring Based on Primal-Dual algorithm

2018 ◽  
Vol 55 (4) ◽  
pp. 041003
Author(s):  
杨爱萍 Yang Aiping ◽  
张越 Zhang Yue ◽  
王金斌 Wang Jinbin ◽  
何宇清 He Yuqing
Keyword(s):  
Total Variation ◽  
Image Deblurring ◽  
Dual Algorithm ◽  
Primal Dual

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 Total Variation Wavelet-Based Medical Image Denoising

2006 ◽  
Vol 2006 ◽  
pp. 1-6 ◽  
Author(s):  
Yang Wang ◽  
Haomin Zhou
Keyword(s):  
Image Denoising ◽  
Total Variation ◽  
Medical Image ◽  
Medical Images ◽  
Stopping Time ◽  
Noise Removal ◽  
Total Variation Minimization ◽  
Time Criterion ◽  
Minimization Scheme

We propose a denoising algorithm for medical images based on a combination of the total variation minimization scheme and the wavelet scheme. We show that our scheme offers effective noise removal in real noisy medical images while maintaining sharpness of objects. More importantly, this scheme allows us to implement an effective automatic stopping time criterion.

scholarly journals An Alternating Direction Method for Mixed Gaussian Plus Impulse Noise Removal

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Si Wang ◽  
Ting-Zhu Huang ◽  
Xi-le Zhao ◽  
Jun Liu
Keyword(s):  
Total Variation ◽  
Numerical Experiments ◽  
Impulse Noise ◽  
State Of The Art ◽  
Noise Removal ◽  
Alternating Direction Method ◽  
Impulse Noise Removal ◽  
Alternating Direction ◽  
Total Variation Model ◽  
Blurred Images

A combined total variation and high-order total variation model is proposed to restore blurred images corrupted by impulse noise or mixed Gaussian plus impulse noise. We attack the proposed scheme with an alternating direction method of multipliers (ADMM). Numerical experiments demonstrate the efficiency of the proposed method and the performance of the proposed method is competitive with the existing state-of-the-art methods.

scholarly journals A Decision-Based Modified Total Variation Diffusion Method for Impulse Noise Removal

2017 ◽  
Vol 2017 ◽  
pp. 1-20 ◽  
Author(s):  
Hongyao Deng ◽  
Qingxin Zhu ◽  
Xiuli Song ◽  
Jinsong Tao
Keyword(s):  
Total Variation ◽  
Impulse Noise ◽  
Impulsive Noise ◽  
Noise Removal ◽  
Diffusion Method ◽  
Median Filtering ◽  
Noise Characteristics ◽  
Weighted Total Variation ◽  
Salt And Pepper

Impulsive noise removal usually employs median filtering, switching median filtering, the total variation L1 method, and variants. These approaches however often introduce excessive smoothing and can result in extensive visual feature blurring and thus are suitable only for images with low density noise. A new method to remove noise is proposed in this paper to overcome this limitation, which divides pixels into different categories based on different noise characteristics. If an image is corrupted by salt-and-pepper noise, the pixels are divided into corrupted and noise-free; if the image is corrupted by random valued impulses, the pixels are divided into corrupted, noise-free, and possibly corrupted. Pixels falling into different categories are processed differently. If a pixel is corrupted, modified total variation diffusion is applied; if the pixel is possibly corrupted, weighted total variation diffusion is applied; otherwise, the pixel is left unchanged. Experimental results show that the proposed method is robust to different noise strengths and suitable for different images, with strong noise removal capability as shown by PSNR/SSIM results as well as the visual quality of restored images.

scholarly journals Crosscorrelation and DOA Estimation for L-Shaped Array via Decoupled Atomic Norm Minimization

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yu Zhang ◽  
Yinan Sun ◽  
Gong Zhang ◽  
Xinhai Wang ◽  
Yu Tao
Keyword(s):  
Prior Information ◽  
Doa Estimation ◽  
Phase Method ◽  
Second Phase ◽  
Two Dimensional ◽  
Two Phase ◽  
Norm Minimization ◽  
Atomic Norm ◽  
Matrix Reconstruction ◽  
Source Number

A novel two-phase method for two-dimensional (2D) direction-of-arrival (DOA) estimation with L-shaped array based on decoupled atomic norm minimization (DANM) is proposed in this paper. In the first phase, given the sample crosscorrelation matrix, the gridless DANM technique considering the noise and finite snapshots effects is employed to exploit the structure and sparse properties of the crosscorrelation matrix. The resulting DANM-based algorithm not only enables the crosscorrelation matrix reconstruction (CCMR) but also reconstructs the covariance matrix of the L-shaped array. Hence, sequentially, in the second phase, the conventional 2D DOA estimators for the L-shaped array can be adopted for the angle estimation. With appropriate 2D DOA estimators, the resulting proposed algorithms can not only achieve better performance but also detect more source number, compared with conventional crosscorrelation-based DOA estimators. Moreover, the proposed method, termed CCMR-DANM, not only has blind characteristic that it does not require the prior information of source numbers but also is more efficient than the existing CCMR-based counterparts. Numerical simulations demonstrate the effectiveness and outperformance of the proposed method.

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