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 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 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 Poisson noisy image restoration via overlapping group sparse and nonconvex second-order total variation priors

PLoS ONE ◽  
2021 ◽  
Vol 16 (4) ◽  
pp. e0250260
Author(s):  
Kyongson Jon ◽  
Jun Liu ◽  
Xiaoguang Lv ◽  
Wensheng Zhu
Keyword(s):  
Image Restoration ◽  
Total Variation ◽  
Image Sensor ◽  
Noisy Image ◽  
Iteratively Reweighted Least Squares ◽  
Alternating Direction ◽  
Proposed Model ◽  
Log Likelihood ◽  
Sharp Edges ◽  
Staircase Artifacts

The restoration of the Poisson noisy images is an essential task in many imaging applications due to the uncertainty of the number of discrete particles incident on the image sensor. In this paper, we consider utilizing a hybrid regularizer for Poisson noisy image restoration. The proposed regularizer, which combines the overlapping group sparse (OGS) total variation with the high-order nonconvex total variation, can alleviate the staircase artifacts while preserving the original sharp edges. We use the framework of the alternating direction method of multipliers to design an efficient minimization algorithm for the proposed model. Since the objective function is the sum of the non-quadratic log-likelihood and nonconvex nondifferentiable regularizer, we propose to solve the intractable subproblems by the majorization-minimization (MM) method and the iteratively reweighted least squares (IRLS) algorithm, respectively. Numerical experiments show the efficiency of the proposed method for Poissonian image restoration including denoising and deblurring.

scholarly journals Non-Blind Image Deblurring Method Using Shear High Order Total Variation Norm

2021 ◽  
Vol 26 (6) ◽  
pp. 495-506
Author(s):  
Lixuan LU ◽  
Tao ZHANG
Keyword(s):  
Total Variation ◽  
High Order ◽  
Perceptual Quality ◽  
Total Variation Norm ◽  
Edge Information ◽  
Blind Image Deblurring ◽  
Alternating Direction ◽  
Blind Deblurring ◽  
Proposed Model ◽  
Blind Image

In this paper, we propose a shear high-order gradient (SHOG) operator by combining the shear operator and high-order gradient (HOG) operator. Compared with the HOG operator, the proposed SHOG operator can incorporate more directionality and detect more abundant edge information. Based on the SHOG operator, we extend the total variation (TV) norm to shear high-order total variation (SHOTV), and then propose a SHOTV deblurring model. We also study some properties of the SHOG operator, and show that the SHOG matrices are Block Circulant with Circulant Blocks (BCCB) when the shear angle is [see formula in PDF]. The proposed model is solved efficiently by the alternating direction method of multipliers (ADMM). Experimental results demonstrate that the proposed method outperforms some state-of-the-art non-blind deblurring methods in both objective and perceptual quality.

scholarly journals Remote Sensing Image Stripe Detecting and Destriping Using the Joint Sparsity Constraint with Iterative Support Detection

2019 ◽  
Vol 11 (6) ◽  
pp. 608 ◽  
Author(s):  
Yun-Jia Sun ◽  
Ting-Zhu Huang ◽  
Tian-Hui Ma ◽  
Yong Chen
Keyword(s):  
Remote Sensing ◽  
Real Data ◽  
Total Variation Regularization ◽  
Joint Sparsity ◽  
Alternating Direction ◽  
Proposed Model ◽  
Comparison Results ◽  
Wide Range ◽  
Image Edges ◽  
Full Consideration

Remote sensing images have been applied to a wide range of fields, but they are often degraded by various types of stripes, which affect the image visual quality and limit the subsequent processing tasks. Most existing destriping methods fail to exploit the stripe properties adequately, leading to suboptimal performance. Based on a full consideration of the stripe properties, we propose a new destriping model to achieve stripe detection and stripe removal simultaneously. In this model, we adopt the unidirectional total variation regularization to depict the directional property of stripes and the weighted ℓ 2 , 1 -norm regularization to depict the joint sparsity of stripes. Then, we combine the alternating direction method of multipliers and iterative support detection to solve the proposed model effectively. Comparison results on simulated and real data suggest that the proposed method can remove and detect stripes effectively while preserving image edges and details.

scholarly journals An adaptive model combining a total variation filter and a fractional-order filter for image restoration

2019 ◽  
Vol 13 ◽  
pp. 174830181983305 ◽  
Author(s):  
Yafeng Yang ◽  
Donghong Zhao
Keyword(s):  
Image Restoration ◽  
Total Variation ◽  
Fractional Order ◽  
Gradient Algorithm ◽  
Remarkable Effect ◽  
Order Filter ◽  
Model Combining ◽  
Proposed Model ◽  
Primal Dual ◽  
Image Edges

In this paper, we propose a model that combines a total variation filter with a fractional-order filter, which can unite the advantages of the two filters, and has a remarkable effect in the protection of image edges and texture details; simultaneously, the proposed model can eliminate the staircase effect. In addition, the model improves the PSNR compared with the total variation filter and the fractional-order filter when removing noise. Zhu and Chan presented the primal-dual hybrid gradient algorithm and proved that it is effective for the total variation filter. On the basis of their work, we employ the primal-dual hybrid gradient algorithm to solve the combined model in this article. The final experimental results show that the new model and algorithm are effective for image restoration.

scholarly journals A Dictionary Learning Method with Total Generalized Variation for MRI Reconstruction

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Hongyang Lu ◽  
Jingbo Wei ◽  
Qiegen Liu ◽  
Yuhao Wang ◽  
Xiaohua Deng
Keyword(s):  
Dictionary Learning ◽  
Image Features ◽  
Sparse Regularization ◽  
Oil Painting ◽  
Total Generalized Variation ◽  
Splitting Technique ◽  
Current State ◽  
Alternating Direction ◽  
Proposed Model ◽  
Generalized Variation

Reconstructing images from their noisy and incomplete measurements is always a challenge especially for medical MR image with important details and features. This work proposes a novel dictionary learning model that integrates two sparse regularization methods: the total generalized variation (TGV) approach and adaptive dictionary learning (DL). In the proposed method, the TGV selectively regularizes different image regions at different levels to avoid oil painting artifacts largely. At the same time, the dictionary learning adaptively represents the image features sparsely and effectively recovers details of images. The proposed model is solved by variable splitting technique and the alternating direction method of multiplier. Extensive simulation experimental results demonstrate that the proposed method consistently recovers MR images efficiently and outperforms the current state-of-the-art approaches in terms of higher PSNR and lower HFEN values.

scholarly journals High-order total variation regularization approach for axially symmetric object tomography from a single radiograph

2015 ◽  
Vol 9 (1) ◽  
pp. 55-77 ◽  
Author(s):  
Raymond H. Chan ◽  
◽  
Haixia Liang ◽  
Suhua Wei ◽  
Mila Nikolova ◽  
...  
Keyword(s):  
Total Variation ◽  
High Order ◽  
Total Variation Regularization ◽  
Axially Symmetric

scholarly journals Infrared Image Deblurring via High-Order Total Variation and Lp-Pseudonorm Shrinkage

2020 ◽  
Vol 10 (7) ◽  
pp. 2533 ◽  
Author(s):  
Jingjing Yang ◽  
Yingpin Chen ◽  
Zhifeng Chen
Keyword(s):  
Total Variation ◽  
Infrared Image ◽  
Noise Pollution ◽  
Image Deblurring ◽  
High Order ◽  
L1 Norm ◽  
Alternating Direction ◽  
Image Blurring ◽  
Image Gradients ◽  
Staircase Artifacts

The quality of infrared images is affected by various degradation factors, such as image blurring and noise pollution. Anisotropic total variation (ATV) has been shown to be a good regularization approach for image deblurring. However, there are two main drawbacks in ATV. First, the conventional ATV regularization just considers the sparsity of the first-order image gradients, thus leading to staircase artifacts. Second, it employs the L1-norm to describe the sparsity of image gradients, while the L1-norm has a limited capacity of depicting the sparsity of sparse variables. To address these limitations of ATV, a high-order total variation is introduced in the ATV deblurring model and the Lp-pseudonorm is adopted to depict the sparsity of low- and high-order total variation. In this way, the recovered image can fit the image priors with clear edges and eliminate the staircase artifacts of the ATV model. The alternating direction method of multipliers is used to solve the proposed model. The experimental results demonstrate that the proposed method does not only remove blurs effectively but is also highly competitive against the state-of-the-art methods, both qualitatively and quantitatively.

Sign in / Sign up

Export Citation Format

Share Document