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 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.

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.

scholarly journals Total Variation Regularization of Matrix-Valued Images

2007 ◽  
Vol 2007 ◽  
pp. 1-11 ◽  
Author(s):  
Oddvar Christiansen ◽  
Tin-Man Lee ◽  
Johan Lie ◽  
Usha Sinha ◽  
Tony F. Chan
Keyword(s):  
Total Variation ◽  
Diffusion Tensor ◽  
Natural Extension ◽  
Positive Definiteness ◽  
Total Variation Regularization ◽  
Diffusion Matrix ◽  
Proposed Model ◽  
Total Variation Model ◽  
Diffusion Tensor Images ◽  
Restoration Model

We generalize the total variation restoration model, introduced by Rudin, Osher, and Fatemi in 1992, to matrix-valued data, in particular, to diffusion tensor images (DTIs). Our model is a natural extension of the color total variation model proposed by Blomgren and Chan in 1998. We treat the diffusion matrixDimplicitly as the productD=LLT, and work with the elements ofLas variables, instead of working directly on the elements ofD. This ensures positive definiteness of the tensor during the regularization flow, which is essential when regularizing DTI. We perform numerical experiments on both synthetical data and 3D human brain DTI, and measure the quantitative behavior of the proposed model.

scholarly journals Speckle Noise Removal by Energy Models with New Regularization Setting

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Bo Chen ◽  
Jinbin Zou ◽  
Weiqiang Zhang
Keyword(s):  
Total Variation ◽  
Ultrasound Image ◽  
Speckle Noise ◽  
Noise Removal ◽  
Energy Models ◽  
Energy Diffusion ◽  
Total Variation Model ◽  
Local Coordinates ◽  
Diffusion Speed ◽  
Adaptive Total Variation

In this paper, we introduce two novel total variation models to deal with speckle noise in ultrasound image in order to retain the fine details more effectively and to improve the speed of energy diffusion during the process. Firstly, two new convex functions are introduced as regularization term in the adaptive total variation model, and then, the diffusion performances of Hypersurface Total Variation (HYPTV) model and Logarithmic Total Variation (LOGTV) model are analyzed mathematically through the physical characteristics of local coordinates. We have shown that the larger positive parameter in the model is set, the greater energy diffusion speed appears to be, but it will cause the image to be too smooth that required adequate attention. Numerical experimental results show that our proposed LOGTV model for speckle noise removal is superior to traditional models, not only in visual effect but also in quantitative measures.

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.

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 Combined total variation of first and fractional orders for Poisson noise removal in digital images

2021 ◽  
pp. 10-19
Author(s):  
Cong Pham ◽  
Thi Thu Tran ◽  
Minh Pham ◽  
Thanh Cong Nguyen
Keyword(s):  
Image Reconstruction ◽  
Image Restoration ◽  
Total Variation ◽  
Fractional Order ◽  
Optimization Problem ◽  
Poisson Noise ◽  
Experimental Results ◽  
First Order ◽  
Proposed Model ◽  
Total Variation Model

Introduction: Many methods have been proposed to handle the image restoration problem with Poisson noise. A popular approach to Poissonian image reconstruction is the one based on Total Variation. This method can provide significantly sharp edges and visually fine images, but it results in piecewise-constant regions in the resulting images. Purpose: Developing an adaptive total variation-based model for the reconstruction of images contaminated by Poisson noise, and an algorithm for solving the optimization problem. Results: We proposed an effective way to restore images degraded by Poisson noise. Using the Bayesian framework, we proposed an adaptive model based on a combination of first-order total variation and fractional order total variation. The first-order total variation model is efficient for suppressing the noise and preserving the keen edges simultaneously. However, the first-order total variation method usually causes artifact problems in the obtained results. To avoid this drawback, we can use high-order total variation models, one of which is the fractional-order total variation-based model for image restoration. In the fractional-order total variation model, the derivatives have an order greater than or equal to one. It leads to the convenience of computation with a compact discrete form. However, methods based on the fractional-order total variation may cause image blurring. Thus, the proposed model incorporates the advantages of two total variation regularization models, having a significant effect on the edge-preserving image restoration. In order to solve the considered optimization problem, the Split Bregman method is used. Experimental results are provided, demonstrating the effectiveness of the proposed method.  Practical relevance: The proposed method allows you to restore Poissonian images preserving their edges. The presented numerical simulation demonstrates the competitive performance of the model proposed for image reconstruction. Discussion: From the experimental results, we can see that the proposed algorithm is effective in suppressing noise and preserving the image edges. However, the weighted parameters in the proposed model were not automatically selected at each iteration of the proposed algorithm. This requires additional research.

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.

Sign in / Sign up

Export Citation Format

Share Document