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.

scholarly journals Infrared Image Super-Resolution Reconstruction Based on Quaternion Fractional Order Total Variation with Lp Quasinorm

2018 ◽  
Vol 8 (10) ◽  
pp. 1864 ◽  
Author(s):  
Xingguo Liu ◽  
Yingpin Chen ◽  
Zhenming Peng ◽  
Juan Wu ◽  
Zhuoran Wang
Keyword(s):  
Total Variation ◽  
Fractional Order ◽  
Infrared Image ◽  
Super Resolution ◽  
Objective Evaluation ◽  
Imaging Systems ◽  
Infrared Images ◽  
Alternating Direction ◽  
Image Super Resolution ◽  
Staircase Artifacts

Owing to the limitations of the imaging principle as well as the properties of imaging systems, infrared images often have some drawbacks, including low resolution, a lack of detail, and indistinct edges. Therefore, it is essential to improve infrared image quality. Considering the information of neighbors, a description of sparse edges, and by avoiding staircase artifacts, a new super-resolution reconstruction (SRR) method is proposed for infrared images, which is based on fractional order total variation (FTV) with quaternion total variation and the L p quasinorm. Our proposed method improves the sparsity exploitation of FTV, and efficiently preserves image structures. Furthermore, we adopt the plug-and-play alternating direction method of multipliers (ADMM) and the fast Fourier transform (FFT) theory for the proposed method to improve the efficiency and robustness of our algorithm; in addition, an accelerated step is adopted. Our experimental results show that the proposed method leads to excellent performances in terms of an objective evaluation and the subjective visual effect.

scholarly journals Performance of relaxed iterative methods for image deblurring problems

2019 ◽  
Vol 13 ◽  
pp. 174830261986173 ◽  
Author(s):  
Jae H Yun
Keyword(s):  
Fixed Point ◽  
Iterative Methods ◽  
Total Variation ◽  
Numerical Experiments ◽  
Krylov Subspace ◽  
Image Deblurring ◽  
Total Variation Regularization ◽  
L1 Norm ◽  
Split Bregman ◽  
Relaxation Parameters

In this paper, we consider performance of relaxation iterative methods for four types of image deblurring problems with different regularization terms. We first study how to apply relaxation iterative methods efficiently to the Tikhonov regularization problems, and then we propose how to find good preconditioners and near optimal relaxation parameters which are essential factors for fast convergence rate and computational efficiency of relaxation iterative methods. We next study efficient applications of relaxation iterative methods to Split Bregman method and the fixed point method for solving the L1-norm or total variation regularization problems. Lastly, we provide numerical experiments for four types of image deblurring problems to evaluate the efficiency of relaxation iterative methods by comparing their performances with those of Krylov subspace iterative methods. Numerical experiments show that the proposed techniques for finding preconditioners and near optimal relaxation parameters of relaxation iterative methods work well for image deblurring problems. For the L1-norm and total variation regularization problems, Split Bregman and fixed point methods using relaxation iterative methods perform quite well in terms of both peak signal to noise ratio values and execution time as compared with those using Krylov subspace methods.

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 Image Deblurring under Impulse Noise via Total Generalized Variation and Non-Convex Shrinkage

Algorithms ◽  
2019 ◽  
Vol 12 (10) ◽  
pp. 221
Author(s):  
Lin ◽  
Chen ◽  
Chen ◽  
Yu
Keyword(s):  
Total Variation ◽  
Impulse Noise ◽  
Signal To Noise Ratio ◽  
Image Deblurring ◽  
L1 Norm ◽  
Signal To Noise ◽  
Total Generalized Variation ◽  
First Order ◽  
Norm Constraint ◽  
Generalized Variation

Image deblurring under the background of impulse noise is a typically ill-posed inverse problem which attracted great attention in the fields of image processing and computer vision. The fast total variation deconvolution (FTVd) algorithm proved to be an effective way to solve this problem. However, it only considers sparsity of the first-order total variation, resulting in staircase artefacts. The L1 norm is adopted in the FTVd model to depict the sparsity of the impulse noise, while the L1 norm has limited capacity of depicting it. To overcome this limitation, we present a new algorithm based on the Lp-pseudo-norm and total generalized variation (TGV) regularization. The TGV regularization puts sparse constraints on both the first-order and second-order gradients of the image, effectively preserving the image edge while relieving undesirable artefacts. The Lp-pseudo-norm constraint is employed to replace the L1 norm constraint to depict the sparsity of the impulse noise more precisely. The alternating direction method of multipliers is adopted to solve the proposed model. In the numerical experiments, the proposed algorithm is compared with some state-of-the-art algorithms in terms of peak signal-to-noise ratio (PSNR), structural similarity (SSIM), signal-to-noise ratio (SNR), operation time, and visual effects to verify its superiority.

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 Infrared Small Target Detection via Non-Convex Rank Approximation Minimization Joint l2,1 Norm

2018 ◽  
Vol 10 (11) ◽  
pp. 1821 ◽  
Author(s):  
Landan Zhang ◽  
Lingbing Peng ◽  
Tianfang Zhang ◽  
Siying Cao ◽  
Zhenming Peng
Keyword(s):  
State Of The Art ◽  
Infrared Image ◽  
Dc Programming ◽  
Background Suppression ◽  
Convex Model ◽  
L1 Norm ◽  
Alternating Direction ◽  
Difference Of Convex ◽  
Rank Approximation ◽  
Small Targets

To improve the detection ability of infrared small targets in complex backgrounds, a novel method based on non-convex rank approximation minimization joint l2,1 norm (NRAM) was proposed. Due to the defects of the nuclear norm and l1 norm, the state-of-the-art infrared image-patch (IPI) model usually leaves background residuals in the target image. To fix this problem, a non-convex, tighter rank surrogate and weighted l1 norm are instead utilized, which can suppress the background better while preserving the target efficiently. Considering that many state-of-the-art methods are still unable to fully suppress sparse strong edges, the structured l2,1 norm was introduced to wipe out the strong residuals. Furthermore, with the help of exploiting the structured norm and tighter rank surrogate, the proposed model was more robust when facing various complex or blurry scenes. To solve this non-convex model, an efficient optimization algorithm based on alternating direction method of multipliers (ADMM) plus difference of convex (DC) programming was designed. Extensive experimental results illustrate that the proposed method not only shows superiority in background suppression and target enhancement, but also reduces the computational complexity compared with other baselines.

Sign in / Sign up

Export Citation Format

Share Document