scholarly journals A Convex Variational Model for Restoring SAR Images Corrupted by Multiplicative Noise

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Hanmei Yang ◽  
Jiachang Li ◽  
Lixin Shen ◽  
Jian Lu
Keyword(s):  
Multiplicative Noise ◽  
Variational Model ◽  
Total Variation Regularization ◽  
Dual Algorithm ◽  
Penalty Term ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Primal Dual ◽  
Data Fidelity ◽  
Blurred Images

This paper studies a new convex variational model for denoising and deblurring images with multiplicative noise. Considering the statistical property of the multiplicative noise following Nakagami distribution, the denoising model consists of a data fidelity term, a quadratic penalty term, and a total variation regularization term. Here, the quadratic penalty term is mainly designed to guarantee the model to be strictly convex under a mild condition. Furthermore, the model is extended for the simultaneous denoising and deblurring case by introducing a blurring operator. We also study some mathematical properties of the proposed model. In addition, the model is solved by applying the primal-dual algorithm. The experimental results show that the proposed method is promising in restoring (blurred) images with multiplicative noise.

A new total variation model for restoring blurred and speckle noisy images

2017 ◽  
Vol 15 (02) ◽  
pp. 1750009 ◽  
Author(s):  
Jian Lu ◽  
Yupeng Chen ◽  
Yuru Zou ◽  
Lixin Shen
Keyword(s):  
Total Variation ◽  
Speckle Noise ◽  
Variational Model ◽  
Total Variation Regularization ◽  
Penalty Term ◽  
Proposed Model ◽  
Total Variation Model ◽  
Data Fidelity ◽  
Blurred Images ◽  
Uniqueness Of A Solution

In coherent imaging systems, such as the synthetic aperture radar (SAR), the observed images are affected by multiplicative speckle noise. This paper proposes a new variational model based on I-divergence for restoring blurred images with speckle noise. The model minimizes the sum of an I-divergence data fidelity term, a new quadratic penalty term based on the statistical property of the noise and the total-variation regularization term. The existence and uniqueness of a solution of the proposed model with some other characteristics are analyzed. Furthermore, an iterative algorithm is introduced to solve the proposed variational model. Our numerical experiments indicate that the proposed method performs favorably.

scholarly journals A variational saturation-value model for image decomposition: Illumination and reflectance

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Wei Wang ◽  
Caifei Li
Keyword(s):  
Minimization Problem ◽  
Color Image ◽  
Color Space ◽  
Image Decomposition ◽  
Total Variation Regularization ◽  
Dual Algorithm ◽  
Proposed Model ◽  
Primal Dual ◽  
Fitting In ◽  
Value Model

<p style='text-indent:20px;'>In this paper, we study to decompose a color image into the illumination and reflectance components in saturation-value color space. By considering the spatial smoothness of the illumination component, the total variation regularization of the reflectance component, and the data-fitting in saturation-value color space, we develop a novel variational saturation-value model for image decomposition. The main aim of the proposed model is to formulate the decomposition of a color image such that the illumination component is uniform with only brightness information, and the reflectance component contains the color information. We establish the theoretical result about the existence of the solution of the proposed minimization problem. We employ a primal-dual algorithm to solve the proposed minimization problem. Experimental results are shown to illustrate the effectiveness of the proposed decomposition model in saturation-value color space, and demonstrate the performance of the proposed method is better than the other testing methods.</p>

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 Image Restoration by a Mixed High-Order Total Variation and l1 Regularization Model

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Jianguang Zhu ◽  
Kai Li ◽  
Binbin Hao
Keyword(s):  
Total Variation ◽  
High Order ◽  
Variational Model ◽  
Total Variation Regularization ◽  
Current State ◽  
Model Combining ◽  
Alternating Direction ◽  
Proposed Model ◽  
Sharp Edges ◽  
Thresholding Algorithm

Total variation regularization is well-known for recovering sharp edges; however, it usually produces staircase artifacts. In this paper, in order to overcome the shortcoming of total variation regularization, we propose a new variational model combining high-order total variation regularization and l1 regularization. The new model has separable structure which enables us to solve the involved subproblems more efficiently. We propose a fast alternating method by employing the fast iterative shrinkage-thresholding algorithm (FISTA) and the alternating direction method of multipliers (ADMM). Compared with some current state-of-the-art methods, numerical experiments show that our proposed model can significantly improve the quality of restored images and obtain higher SNR and SSIM values.

A second-order nonlocal regularized variational model for multiframe image super-resolution

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Amine Laghrib ◽  
Fatimzehrae Aitbella ◽  
Abdelilah Hakim
Keyword(s):  
Super Resolution ◽  
Image Texture ◽  
Variational Model ◽  
Dual Algorithm ◽  
Tv Regularization ◽  
Nonlocal Total Variation ◽  
Primal Dual ◽  
Image Super Resolution ◽  
Image Edges ◽  
Well Posed

Abstract In this paper, we propose a new nonlocal super-resolution (SR) model which is a combination of the nonlocal total variation (TV) regularization and the nonlocal p-Laplacian term (with p = 2). This choice is motivated by the success of the nonlocal TV term in preserving image edges and the efficiency of the nonlocal p-Laplacian term in preserving the image texture. To ensure the convergence of the proposed optimization SR problem, we prove the existence and uniqueness of a solution in a well-posed framework. In addition, to resolve the encountered minimization problem, we proposed a modified primal-dual algorithm and numerical results are also given to show the performance of the proposed approach.

New Hybrid Variational Recovery Model for Blurred Images with Multiplicative Noise

2013 ◽  
Vol 3 (4) ◽  
pp. 263-282 ◽  
Author(s):  
Yiqiu Dong ◽  
Tieyong Zeng
Keyword(s):  
Multiplicative Noise ◽  
Noise Removal ◽  
Variational Model ◽  
Convex Model ◽  
Split Bregman ◽  
New Approach ◽  
Uniqueness Of The Solution ◽  
Minimisation Problem ◽  
The Stability ◽  
Blurred Images

AbstractA new hybrid variational model for recovering blurred images in the presence of multiplicative noise is proposed. Inspired by previous work on multiplicative noise removal, an I-divergence technique is used to build a strictly convex model under a condition that ensures the uniqueness of the solution and the stability of the algorithm. A split-Bregman algorithm is adopted to solve the constrained minimisation problem in the new hybrid model efficiently. Numerical tests for simultaneous deblurring and denoising of the images subject to multiplicative noise are then reported. Comparison with other methods clearly demonstrates the good performance of our new approach.

scholarly journals Multiplicative Noise Removal Based on the Linear Alternating Direction Method for a Hybrid Variational Model

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Yan Hao ◽  
Jianlou Xu ◽  
Fengyun Zhang ◽  
Xiaobo Zhang
Keyword(s):  
Total Variation ◽  
Multiplicative Noise ◽  
Splitting Method ◽  
Noise Removal ◽  
Variational Model ◽  
Total Variation Regularization ◽  
Alternating Direction ◽  
Staircase Effect ◽  
Multiplicative Noise Removal ◽  
Alternative Direction Method

To preserve the edge, multiplicative noise removal models based on the total variation regularization have been widely studied, but they suffer from the staircase effect. In this paper, to preserve the edge and reduce the staircase effect, we develop a hybrid variational model based on the variable splitting method for multiplicative noise removal; the new model is a strictly convex objective function which contains the total variation regularization and a modified regularization term. We use the linear alternative direction method to find the minimal solution and also give the convergence proof of the proposed algorithm. Experimental results verify that the proposed model can obtain the better results for removing the multiplicative noise compared with the recent method.

A Two-Stage Image Segmentation Model for Multi-Channel Images

2016 ◽  
Vol 19 (4) ◽  
pp. 904-926 ◽  
Author(s):  
Zhi Li ◽  
Tieyong Zeng
Keyword(s):  
Image Segmentation ◽  
Minimal Surface ◽  
Hill Climbing ◽  
Variational Model ◽  
Two Stage ◽  
Dual Approach ◽  
Second Stage ◽  
Primal Dual ◽  
Data Fidelity ◽  
Number Of Segments

AbstractThis paper introduces a two-stage model for multi-channel image segmentation, which is motivated by minimal surface theory. Indeed, in the first stage, we acquire a smooth solutionufrom a convex variational model related to minimal surface property and different data fidelity terms are considered. This minimization problem is solved efficiently by the classical primal-dual approach. In the second stage, we adopt thresholding to segment the smoothed imageu. Here, instead of using K-means to determine the thresholds, we propose a more stable hill-climbing procedure to locate the peaks on the 3D histogram ofuas thresholds, in the meantime, this algorithm can also detect the number of segments. Finally, numerical results demonstrate that the proposed method is very robust against noise and superior to other image segmentation approaches.

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