Fast alternating direction method of multipliers for total-variation-based image restoration

A novel algorithm, i.e. the fast alternating direction method of multipliers （ADMM）, is applied to solve the classical total-variation （ TV ）-based model for image reconstruction. First, the TV-based model is reformulated as a linear equality constrained problem where the objective function is separable. Then, by introducing the augmented Lagrangian function, the two variables are alternatively minimized by the Gauss-Seidel idea. Finally, the dual variable is updated. Because the approach makes full use of the special structure of the problem and decomposes the original problem into several low-dimensional sub-problems, the per iteration computational complexity of the approach is dominated by two fast Fourier transforms. Elementary experimental results indicate that the proposed approach is more stable and efficient compared with some state-of-the-art algorithms.

A new two-step variational model for multiplicative noise removal with applications to texture images

Multiplicative noise removal problems have attracted much attention in recent years.Unlike additive noise,multiplicative noise destroys almost all information of the original image,especially for texture images.Motivated by the TV-Stokes model,we propose a new two-step variational model to denoise the texture images corrupted by multiplicative noise with a good geometry explanation in this paper.In the first step,we convert the multiplicative denoising problem into an additive one by the logarithm transform and propagate the isophote directions in the tangential field smoothing.Once the isophote directions are constructed,an image is restored to fit the constructed directions in the second step.The existence and uniqueness of the solution to the variational problems are proved.In these two steps,we use the gradient descent method and construct finite difference schemes to solve the problems.Especially,the augmented Lagrangian method and the fast Fourier transform are adopted to accelerate the calculation.Experimental results show that the proposed model can remove the multiplicative noise efficiently and protect the texture well.

Compressive near-field millimeter wave imaging algorithm based on Gini index and total variation mixed regularization

A compressive near-field millimeter wave(MMW)imaging algorithm is proposed.From the compressed sensing(CS)theory,the compressive near-field MMW imaging process can be considered to reconstruct an image from the under-sampled sparse data.The Gini index(GI)has been founded that it is the only sparsity measure that has all sparsity attributes that are called Robin Hood,Scaling,Rising Tide,Cloning,Bill Gates,and Babies.By combining the total variation(TV)operator,the GI-TV mixed regularization introduced compressive near-field MMW imaging model is proposed.In addition,the corresponding algorithm based on a primal-dual framework is also proposed.Experimental results demonstrate that the proposed GI-TV mixed regularization algorithm has superior convergence and stability performance compared with the widely used l1-TV mixed regularization algorithm.

Image reconstruction based on total-variation minimization and alternating direction method in linear scan computed tomography

Linear scan computed tomography （LCT） is of great benefit to online industrial scanning and security inspection due to its characteristics of straight-line source trajectory and high scanning speed. However, in practical applications of LCT, there are challenges to image reconstruction due to limited-angle and insufficient data. In this paper, a new reconstruction algorithm based on total-variation （TV） minimization is developed to reconstruct images from limited-angle and insufficient data in LCT. The main idea of our approach is to reformulate a TV problem as a linear equality constrained problem where the objective function is separable, and then minimize its augmented Lagrangian function by using alternating direction method （ADM） to solve subproblems. The proposed method is robust and efficient in the task of reconstruction by showing the convergence of ADM. The numerical simulations and real data reconstructions show that the proposed reconstruction method brings reasonable performance and outperforms some previous ones when applied to an LCT imaging problem.

Dark channel prior based blurred image restoration method using total variation and morphology

The blurred image restoration method can dramatically highlight the image details and enhance the global contrast, which is of benefit to improvement of the visual effect during practical ap- plications. This paper is based on the dark channel prior principle and aims at the prior information absent blurred image degradation situation. A lot of improvements have been made to estimate the transmission map of blurred images. Since the dark channel prior principle can effectively restore the blurred image at the cost of a large amount of computation, the total variation （TV） and image morphology transform （specifically top-hat transform and bottom- hat transform） have been introduced into the improved method. Compared with original transmission map estimation methods, the proposed method features both simplicity and accuracy. The es- timated transmission map together with the element can restore the image. Simulation results show that this method could inhibit the ill-posed problem during image restoration, meanwhile it can greatly improve the image quality and definition.

Image decomposition and staircase effect reduction based on total generalized variation

Total variation （TV） is widely applied in image process-ing. The assumption of TV is that an image consists of piecewise constants, however, it suffers from the so-cal ed staircase effect. In order to reduce the staircase effect and preserve the edges when textures of image are extracted, a new image decomposition model is proposed in this paper. The proposed model is based on the to-tal generalized variation method which involves and balances the higher order of the structure. We also derive a numerical algorithm based on a primal-dual formulation that can be effectively imple-mented. Numerical experiments show that the proposed method can achieve a better trade-off between noise removal and texture extraction, while avoiding the staircase effect efficiently.

Total Variation Constrained Non-Negative Matrix Factorization for Medical Image Registration

This paper presents a novel medical image registration algorithm named total variation constrained graphregularization for non-negative matrix factorization(TV-GNMF).The method utilizes non-negative matrix factorization by total variation constraint and graph regularization.The main contributions of our work are the following.First,total variation is incorporated into NMF to control the diffusion speed.The purpose is to denoise in smooth regions and preserve features or details of the data in edge regions by using a diffusion coefficient based on gradient information.Second,we add graph regularization into NMF to reveal intrinsic geometry and structure information of features to enhance the discrimination power.Third,the multiplicative update rules and proof of convergence of the TV-GNMF algorithm are given.Experiments conducted on datasets show that the proposed TV-GNMF method outperforms other state-of-the-art algorithms.

Novel image restoration model coupling gradient fidelity term based on adaptive total variation

A novel image restoration model coupling with a gradient fidelity term based on adaptive total variation is proposed in this paper. In order to choose proper parameters, the selection criteria were analyzed theoretically, and a simple scheme to demonstrate its validity was adopted experimentally. To make fair comparisons of performances of three models, the same numerical algorithm was used to solve partial differential equations. Both the international standard test image on Lena and HR image of CBERS-02B of Dalian city were used to verify the performance of the model. Experimental results illustrate that the new model not only preserved the edge and important details but also alleviated the staircase effect effectively.

Multiquadric Radial Basis Function Approximation Scheme for Solution of Total Variation Based Multiplicative Noise Removal Model

This article introduces a fastmeshless algorithm for the numerical solution nonlinear partial differential equations(PDE)by Radial Basis Functions(RBFs)approximation connected with the Total Variation(TV)-basedminimization functional and to show its application to image denoising containing multiplicative noise.These capabilities used within the proposed algorithm have not only the quality of image denoising,edge preservation but also the property of minimization of staircase effect which results in blocky effects in the images.It is worth mentioning that the recommended method can be easily employed for nonlinear problems due to the lack of dependence on a mesh or integration procedure.The numerical investigations and corresponding examples prove the effectiveness of the recommended algorithm regarding the robustness and visual improvement as well as peak-signal-to-noise ratio(PSNR),signal-to-noise ratio(SNR),and structural similarity index(SSIM)corresponded to the current conventional TV-based schemes.

基于稀疏约束TV最小化的CT图像重建

稀疏角度计算机断层扫描成像(computer tomography,CT)图像重建是一种降低CT扫描辐射剂量的重要方式。而经典的用于稀疏角度CT图像重建的广义迭代软阈值(generalizationoftheiterativesoft-thresholding,GIST)算法收敛速度慢,不能满足临床对检查结果实时性的要求。全变分(totalvariation,TV)最小化算法在稀疏角度下既能减少条纹伪影又能较好地保留目标边界。文章提出稀疏约束的全变分算法,利用交替方向乘子法(alternatedirectionmultipliermethod,ADMM),将重建优化问题分解为2个子问题之和,有效提升了重建效果的同时提高了重建速度。实验结果表明:所提出的方法对数字模型图像和实际临床腹部图像都实现了高质量的图像重建,收敛速度较传统的同步迭代方法有大幅提升。

Weighted Variational Minimization Model for Wavelet Domain Inpainting with Primal-Dual Method

To preserve the edges and details of the image,a new variational model for wavelet domain inpainting was proposed which contained a non-convex regularizer. The non-convex regularizer can utilize the local information of image and perform better than those usual convex ones. In addition, to solve the non-convex minimization problem,an iterative reweighted method and a primaldual method were designed. The numerical experiments show that the new model not only gets better visual effects but also obtains higher signal to noise ratio than the recent method.

Low-rank matrix recovery with total generalized variation for defending adversarial examples

Low-rank matrix decomposition with first-order total variation(TV)regularization exhibits excellent performance in exploration of image structure.Taking advantage of its excellent performance in image denoising,we apply it to improve the robustness of deep neural networks.However,although TV regularization can improve the robustness of the model,it reduces the accuracy of normal samples due to its over-smoothing.In our work,we develop a new low-rank matrix recovery model,called LRTGV,which incorporates total generalized variation(TGV)regularization into the reweighted low-rank matrix recovery model.In the proposed model,TGV is used to better reconstruct texture information without over-smoothing.The reweighted nuclear norm and Li-norm can enhance the global structure information.Thus,the proposed LRTGV can destroy the structure of adversarial noise while re-enhancing the global structure and local texture of the image.To solve the challenging optimal model issue,we propose an algorithm based on the alternating direction method of multipliers.Experimental results show that the proposed algorithm has a certain defense capability against black-box attacks,and outperforms state-of-the-art low-rank matrix recovery methods in image restoration.

Non-Blind Image Deblurring via Shear Total Variation Norm

In this paper, we propose a novel shear gradient operator by combining the shear and gradient operators. The shear gradient operator performs well to capture diverse directional information in the image gradient domain. Based on the shear gradient operator, we extend the total variation(TV) norm to the shear total variation(STV) norm by adding two shear gradient terms. Subsequently, we introduce a shear total variation deblurring model. Experimental results are provided to validate the ability of the STV norm to capture the detailed information. Leveraging the Block Circulant with Circulant Blocks(BCCB) structure of the shear gradient matrices, the alternating direction method of multipliers(ADMM) algorithm can be used to solve the proposed model efficiently. Numerous experiments are presented to verify the performance of our algorithm for non-blind image deblurring.

稀疏角度CT图像重建的Huber-TV正则化方法

对于稀疏角度下的投影数据,计算机断层扫描重建图像容易出现分辨率低、伪影较多的问题,难以满足工业及医学诊断要求。文中从迭代重建的角度出发,提出一个结合全变分(TV)和Huber函数(Huber-TV)的CT重建方法。该方法利用Huber函数替代传统全变分模型中的L1范数,在合理控制函数阈值的条件下,充分利用Huber函数的线性部分对大于阈值的梯度图像进行较轻的惩罚,以保持图像边缘连续性;再结合二次项对小于阈值的梯度图像进行较大的惩罚,以抑制图像中不连续梯度跳跃。新模型目标函数的光滑性可以使得梯度下降法快速收敛到最优值,避开传统全变分模型中的次梯度计算,从而降低计算复杂度并加快迭代速度。实验结果表明,在稀疏角度重建条件下,与传统TV模型相比,Huber-TV模型的均方根误差降低19%,信噪比提升22.33 dB,说明所提方法高效可行。

基于分数阶全变分和低秩正则化的彩色图像去模糊方法

针对现有的彩色图像去模糊过程中存在色彩失衡、阶梯效应和伪影等现象,提出了一种基于分数阶全变分和低秩正则的图像去模糊优化方法。首先,将传统的RGB彩色图像转换到YCbCr颜色空间,利用其亮度通道特征解决色彩失衡问题;其次,利用分数阶全变分的特征消除图像恢复任务中出现的阶梯效应,并且引入加权核范数低秩正则进一步抑制伪影及噪声;最后,利用交替方向乘子法设计出高效的求解方法,通过迭代优化得到纯净图像的最优估计。对彩色图像测试的实验结果表明,所提出的方法对图像去模糊任务取得较好的视觉恢复效果,客观评价指标良好。

基于复合正则化的稀疏SAR成像方法研究

随着高分辨率对地观测要求的不断提高,合成孔径雷达(Synthetic Aperture Radar,SAR)的应用将越来越广泛。针对高分辨率SAR成像存在数据量大、存储难度高、计算时间长等问题,目前常用的解决方法是在SAR成像模型中引入压缩感知(Compressed Sensing,CS)的方法降低采样率和数据量。通常使用单一的正则化作为约束条件,可以抑制点目标旁瓣,实现点目标特征增强,但是观测场景中可能存在多种目标类型,因此使用单一正则化约束难以满足多种特征增强的要求。本文提出了一种基于复合正则化的稀疏高分辨SAR成像方法,通过压缩感知降低数据量,并使用多种正则化的线性组合作为约束条件,增强观测场景中不同类型目标的特征,实现复杂场景中高分辨率对地观测的要求。该方法在稀疏SAR成像模型中引入非凸正则化和全变分(Total Variation,TV)正则化作为约束条件,减小稀疏重构误差、增强区域目标的特征,降低噪声对成像结果的影响,提高成像质量;采用改进的交替方向乘子法(Alternating Direction Method of Multipliers,ADMM)实现复合正则化约束的求解,减少计算时间、快速重构图像;使用方位距离解耦算子代替观测矩阵及其共轭转置,进一步降低计算复杂度。仿真和实测数据实验表明,本文所提算法可以对点目标和区域目标进行特征增强,减小计算复杂度,提高收敛性能,实现快速高分辨的图像重构。

基于TV模型的改进算法在图像修复中的应用

基于TV(total variation)模型的修复算法有较好的恢复效果,但对参数的选取比较敏感,且运算量大。文章提出了基于TV模型的改进的自适应算法,可根据破损区域外部参考像素对待修补点的相关度,通过设置不同的参数和权值,将不同形状的待修复区域所用的不同算法统一表示,使其应用范围更广、速度更快;此外,在迭代过程中,设置不同的参数以解决参数选取的敏感问题,从而达到更好的修复效果。实验表明,该算法能高效、稳定地处理破损区域的图像信息。

我国区域用水总量演变规律及驱动效应研究

针对当前我国稳步推进的节水和水网建设的工作需求,以及水资源时空分布严重不均,各地区经济发展水平、人口规模等存在较大差异的特点,利用我国2000-2020年各省级行政区的用水量、产业增加值、人口结构等数据,采用LMDI指数分解法和GDP不变价换算方法,从时间和空间两个角度分析了各分区用水总量、用水结构变化差异以及用水强度、产业结构、经济规模和人口规模四方面驱动效应的强度和贡献比例,旨在支撑我国水资源规划和管理以及用水结构调整。从时间角度,经济增长是我国用水总量增加的最主要驱动因素,行业用水强度降低和产业结构调整尤其是第一产业用水强度和占比的降低是抑制区域用水总量增加的主要因素,其中用水强度效应略大于产业结构效应,而人口规模增加对用水总量增加的作用效果不明显,因此我国的用水量控制应该在提高用水效率、优化升级产业结构的策略上。从空间角度方面,我国各大分区4种驱动效应对用水总量上升的促进或抑制作用稳定,西南、西北等内陆地区需要在优化产业结构的基础上大力发展经济规模,同时西北地区还迫切需要提高第一产业用水效率,而华东地区可适当控制人口规模,东北和西北则需要控制人口流出,以缩小我国各区域用水量的空间差异。

综合自适应阈值与多尺度的TV图像修复方法

基于TV模型的图像修复算法具有较好的修复效果,但其对参数的选取较敏感,且运算量较大。该文提出了一种综合自适应阈值与多尺度的TV图像修复算法,该方法不仅可以提高TV图像修复模型的修复稳定性,还可以进一步压缩运算量,提高修复速度。