Domain Decomposition Methods for Nonlocal Total Variation Image Restoration

Nonlocal total variation (TV) regularization (Gilboa and Osher in Multiscale Model Simulat 7(3): 1005–1028, 2008; Zhou and Schölkopf in Pattern recognition, proceedings of the 27th DAGM symposium. Springer, Berlin, pp 361–368, 2005) has been widely used for the natural image processing, since it is able to preserve repetitive textures and details of images. However, its applications have been limited in practice, due to the high computational cost for large scale problems. In this paper, we apply domain decomposition methods (DDMs) (Xu et al. in Inverse Probl Imag 4(3):523–545, 2010) to the nonlocal TV image restoration. By DDMs, the original problem is decomposed into much smaller subproblems defined on subdomains. Each subproblem can be efficiently solved by the split Bregman algorithm and Bregmanized operator splitting algorithm in Zhang et al. (SIAM J Imaging Sci 3(3):253–276, 2010). Furthermore, by using coloring technique on the domain decomposition, all subproblems defined on subdomains with same colors can be computed in parallel. Our numerical examples demonstrate that the proposed methods can efficiently solve the nonlocal TV based image restoration problems, such as denoising, deblurring and inpainting. It can be computed in parallel with a considerable speedup ratio and speedup efficiency.     

自适应Shearlet域约束的全变差图像去噪

采用传统非线性扩散图像去噪方法得到的图像边缘模糊,为此,提出一种有限自适应Shearlet域约束的极小化变分图像去噪算法。通过自适应阈值收缩Shearlet系数,保留图像纹理与边缘空间,利用全变差极小化平滑空间,建立全变差正则化的能量泛函去噪模型。实验结果表明,该算法能在减少图像噪声的同时,保留图像边缘信息,对含有丰富纹理结构的图像,去噪性能更佳。     

一种基于图像边缘检测的全变分的去噪方法

提出了一种基于边缘检测的全变分图像去噪方法.在利用全变分去噪之前,先用Canny算子检测图像的边缘,对检测出的边缘区域和非边缘区域做标记;然后在边缘和非边缘区域设置不同的均衡系数,利用全变分模型对图像进行去噪.实验结果表明该算法能抑制以往全变分模型方法产生的阶梯效应,具有较好的图像恢复效果.     

Image Denoising and Decomposition with Total Variation Minimization and Oscillatory Functions

In this paper, we propose a new variational model for image denoising and decomposition, witch combines the total variation minimization model of Rudin, Osher and Fatemi from image restoration, with spaces of oscillatory functions, following recent ideas introduced by Meyer. The spaces introduced here are appropriate to model oscillatory patterns of zero mean, such as noise or texture. Numerical results of image denoising, image decomposition and texture discrimination are presented, showing that the new models decompose better a given image, possible noisy, into cartoon and oscillatory pattern of zero mean, than the standard ones. The present paper develops further the models previously introduced by the authors in Vese and Osher (Modeling textures with total variation minimization and oscillating patterns in image processing, UCLA CAM Report 02-19, May 2002, to appear in Journal of Scientific Computing, 2003). Other recent and related image decomposition models are also discussed.     

基于图像亮度局部约束的总变分图像去噪法

为了解决总变分图像去噪方法易产生虚假边缘这一不足,结合总变分理论和图像亮度局部约束的优点,提出了一种新的图像去噪方法。在总变分图像去噪的数值求解过程中,利用局部均值和局部方差对迭代过程中所获得的结果进行局部约束。实验结果表明,本文方法具有良好的图像去噪能力,在高噪声水平下,其峰值信噪比(Peak signal-noise ratio,PSNR)至少提高了1dB左右,图像视觉效果也有了很大改善。     

一种自适应全变分图像去噪算法

针对传统全变分去噪算法存在需要已知噪声方差和阶梯效应的问题,提出一种自适应全变分图像去噪算法。该算法通过修改传统算法中的逼近项,将经模糊处理后的图像代替原含噪声图像,使得在算法的计算过程中不需要已知图像的噪声方差,也减少逼近项因图像噪声所产生的误差影响。并且拉格朗日因子不再是一个全局变量,而是由图像局部信息决定其数值大小,同时用近似的边缘信息对拉格朗日因子进行加权,从而使图像的演化过程可以由统一的演化公式来表示。最后从实验和数据分析的结果可以看出,该算法要明显优于传统的全变分图像去噪算法。     

A Non-Overlapping Domain Decomposition Method for the Advection-Diffusion Problem

The application of a non-overlapping domain decomposition method to the solution of a stabilized finite element method for elliptic boundary value problems is considered. We derive an a-posteriori error estimate which bounds the error on the subdomains by the interface error of the subdomain solutions. As a by-product, some foundation is given to the design of the interface transmission condition. Numerical results support the theoretical results. Furthermore, we adapt a recent result on a-posteriori estimates for singular perturbation problems in order to obtain an a-posteriori estimate for the discrete subdomain solutions.     

一种基于整体变分自适应图像平滑去噪的方法

在图象处理过程中,图象降噪是底层的处理,将影响图像的后继分析处理质量。基于整体变分法的一种自适应TV去噪方法,它根据图像中每一像素点的梯度信息,自适应选取去噪模型中决定平滑强弱的参数P,从而达到较好的去噪效果。仿真实验结果表明方法的有效性。     

基于整体变分图象恢复模型的小波域正则化方法

通过改进小波软阈值收缩的过程,提出了小波框架下的整体变分正则化模型.模型中利用改进小波阈值技术选取合适的需要保留的小波系数,然后对该系数重建图象进行空域各向异性扩散处理.文中提出了该变分问题完整的空域和小波域交替迭代的图象恢复算法.实验证明,该算法不仅具有较强的噪声抑制能力,而且能够保持和增强图象的边缘,大大提高了图象的视觉质量.     

基于小波域维纳滤波的图像降噪技术

传统的小波域局部维纳滤波器的参数由小波系数的某个邻域上的系数或某个邻域上的系数加上相邻尺度上的对应系数所估计,由于邻域不可能取得很大,这样会导致在某些点上估计精度的下降.对此,该文首先分析了传统的小波域局部维纳滤波器的估计误差,然后根据分析的结果,提出了一种对该算法的改进,即先用适当的门限值对小波系数进行阈值化处理,再进行局部维纳滤波.对不同噪声水平的测试图像的仿真结果表明,该改进措施可以有效地改善小波域局部维纳滤波的降噪性能,而且噪声污染越严重,改善越明显.     

Multilevel Threshold Based Image Denoising in Curvelet Domain

Journal of Computer Science and Technology - In this paper, we propose a multilevel thresholding technique for noise removal in curvelet transform domain which uses cycle-spinning. Most of...     

基于非凸低秩矩阵逼近和全变分正则化的高光谱图像去噪

高光谱图像在采集过程中经常受到混合噪声的干扰,严重影响了图像后续应用的性能,因此图像去噪已成为一个极其重要的预处理过程.文中采用非凸正则项代替传统的核范数重新构造逼近问题,使稀疏正则项更贴近本质秩函数的属性,进而提出了一种将非凸代理函数、全变分正则项和l2,1范数集成于统一框架的混合噪声去除算法.所提算法旨在将退化的高...     

基于二维经验模式分解的图像去噪

通过二维经验模式分解(BEMD),可将被噪声污染的图像分解为一系列细节信息和趋势信息.由图像的趋势信息重建图像,可达到去除图像噪声的目的.实验结果表明该方法对去除高斯白噪声、乘性噪声具有较好的效果,峰值信噪比(PSNR)得到明显提高.     

基于贝叶斯估计的Contourlet域图像降噪方法

提出了一种基于贝叶斯估计的Contourlet域图像降噪方法。该方法对输入的带噪图像进行多尺度、多方向的Contourlet稀疏分解,并在Contourlet域利用最小Bayesian风险函数对分解系数进行估计,通过Contourlet反变换得到预降噪图像。实验结果表明,该方法较其他的Contourlet域收缩阈值降噪效果好,进一步提高了PSNR值和降低了MSE值,能获得更好的图像恢复的质量。     

一种基于领域阈值的小波图像去噪算法

为了去除图像中的噪声,文章利用图像分块的思想,结合阈值去噪法和最小均方误差估计(MMSE),给出了一种基于领域阈值的小波域图像去噪算法。该算法与经典的子带自适应阈值去噪法BayesShrink算法相比,本文算法在峰值信噪比和视觉效果上都好于BayesShrink算法。     

基于Contourlet域主成分分析的SAR图像去噪

相干斑噪声是合成孔径雷达图像所固有的,并且严重降低了图像的可编译性,影响了后续图像分割,特征提取,目标分类和识别等工作.因此,SAR图像的相干斑去除问题一直是SAR图像应用研究的重要问题之一.针对SAR图像噪声去除问题,提出了一种基于Contourlet多尺度分解域主成分分析的SAR图像去噪新方法,并且简要归纳了已有的SAR图像去噪方法.方法首先对源图像进行Contourlet分解,在不同频段的子带图像中,利用主成分分析方法进行能量保持,用重构图像来进行子带去噪,最后通过Contourlet逆变换得到去噪之后的图像.在SAR图像上的实验结果表明,方法不仅较好地保持了图像的纹理和细节特征,且信噪比也较高.     

Total Generalized Variation Based Denoising Models for Ultrasound Images

In this paper, we introduce a class of variational models for the restoration of ultrasound images corrupted by noise. The proposed models involve the convex or nonconvex total generalized variation regularization. The total generalized variation regularization ameliorates the staircasing artifacts that appear in the restored images of total variation based models. Incorporating total generalized variation regularization with nonconvexity helps preserve edges in the restored images. To realize the proposed convex model, we adopt the alternating direction method of multipliers, and the iteratively reweighted \(\ell _1\) algorithm is employed to handle the nonconvex model. These methods result in fast and efficient optimization algorithms for solving our models. Numerical experiments demonstrate that the proposed models are superior to other state-of-the-art models.     

基于整体变分的图像修复研究

图像修复是指对数字图像中丢失破损的部分进行还原,是一种很早出现的工艺技术。目前,图像修复技术有了巨大的发展。本文从基本理论、模型建立和数值计算方面介绍了基于总体变分的图像修复算法。