基于曲率差分的自适应全变分去噪算法

针对整体变分（TV）修复模型易受到梯度的影响而且常常会丢失图像细节信息的缺点,提出了一种基于曲率差分的自适应全变分去噪算法。在联合非线性各向异性扩散滤波器和冲击滤波器对含噪图像做预处理的基础上,通过自适应方式调节正则项和保真项的权重系数,该算法能同时兼顾边缘保留和图像平滑去噪。仿真实验结果表明：与现有的去噪算法相比,该算法在不同强度的脉冲噪声下可以将峰值信噪比提升14%以上,同时将归一均方误差降低43%以上。     

一种抑制图像阶梯效应的改进全变分去噪方法

针对全变分图像去噪算法中处理边缘区域与平滑区域相互冲突从而导致阶梯效应的问题,提出利用局部梯度阈值对两者进行分开滤波去噪的方法。在分析现有利用小波变换进行噪声预测的基础上,提出更精确的改进预测算法;通过实验,得到局部梯度阈值与噪声方差的关系方程,以及最优梯度阈值的估算方法;给出改进算法的步骤与迭代方法。实验结果表明,该算法能有效去除图像上的高斯噪声、获得较好的边缘保护效果,同时能克服全变分去噪后复原图像出现阶梯效应的问题。     

自适应残差图像的分数阶全变分去噪算法

目的 全变分（TV）去噪模型具有较好的去噪效果,但对于图像的弱边缘和纹理细节的保持不够理想。自适应分数阶全变分（AFTV）模型根据图像局部信息,区分图像的纹理区域和非纹理区域,自适应计算投影算法中的软阈值,可较好地保持图像的弱边缘和纹理细节,但该方法当噪声增大时“阶梯”效应比较明显,弱边缘和纹理细节保持效果不够理想。针对该问题,提出一种改进的分数阶全变分去噪算法。方法 该算法在计算残差图像时,用分数阶全变分模型替代整数一阶全变分模型,并根据较精确的残差图像的局部方差区分图像纹理区域和平坦区域,使保真项参数的自适应选取更加合理,提高了算法的去噪性能。结果 针对3种不同类型的噪声图像,将本文模型与TV模型和AFTV模型进行对比实验,并采用峰值信噪比（PSNR）和结构相似性（SSIM）评定去噪效果和纹理保持能力。对于高斯噪声图像,本文算法在PSNR方面比TV模型和AFTV模型分别可平均提高2.72 dB和1.38 dB,SSIM分别可平均提高0.047和0.020。对于椒盐噪声图像,本文算法结合中值滤波算法在PSNR和SSIM方面比传统中值滤波算法分别可平均提高1.308 dB和0.011。对于泊松噪声图像,本文算法在PSNR、SSIM方面与AFTV较接近,比TV分别可提高1.59 dB和0.005。结论 通过对添加不同类型的噪声图像进行实验,结果表明提出的算法在去噪性能上与TV和AFTV相比均有较大提高,尤其对于噪声较大的图像效果更为显著,在去噪效率上与AFTV的时间复杂度相当,时耗接近略有降低。且本文算法普适性较好,能有效去除多种典型类型的噪声。     

基于噪声检测的总变分去噪算法

对受高斯和脉冲混合噪声污染的数字图像去噪方法进行了研究,提出了一种基于噪声检测的自适应总变分(TV)去噪算法。提出的改进算法采用两步迭代框架实现:脉冲噪点检测和全变分图像恢复。第一步中,考虑到脉冲噪声污染的像素点不包含原图像有效信息,采用一种局部统计值,即邻域像素间的随机绝对差排序值(ROAD)估计出噪点的位置;第二步中,采用L2-TV方法进行去噪处理,并对上述过程进行迭代处理,得到去噪图像。在噪点估计过程中引入脉冲噪点水平参数,这样处理的优势在于可更准确地检测出脉冲噪点;而L2-TV去噪方法可很好地去除高斯噪声,两者结合有效地解决了TV算法存在误判图像脉冲噪声为边缘而产生假边缘的问题。与现有典型去噪方法的比较实验表明,该迭代去噪算法,即TV-ROAD算法,既能够去除混合噪声,又可以保留图像细节特征。     

基于自适应投影算法的分数阶全变分去噪模型*

为了在图像去噪的同时较好地保持图像的弱边缘和纹理细节,提出基于自适应投影算法的分数阶全变分模型.该模型使用Grünwald-Letnikov分数阶微分替代全变分正则项中的一阶导数,通过将图像投影在全变分球体上以解决分数阶全变分的优化问题.并根据图像的局部信息将图像分为纹理区域和非纹理区域,从而自适应计算投影方法中的软阈值.理论分析和实验均表明,文中方法在去除噪声的同时可以消除块效应,并且能有效保持图像的弱边缘和纹理细节.     

基于小波包分解的整体变分去噪算法

由Rudin等人提出的整体变分（TV）模型被认为是目前最好的图像去噪模型之一。理论表明,TV模型对分块常量的图像去噪效果显著。对于纹理细节丰富的图像,通过引入小波包分解技术,对图像的纹理细节进行多层小波包分解,得到一系列近似分块常量的子图像,用TV模型对子图像分别进行处理,从而图像的纹理细节得到了更好的保留。相对于单独使用TV模型去噪,该方法得到的复原图像峰值信噪比（PSNR）提高了1 dB左右。同时由于采用改进的Bregman迭代方案求解TV模型,算法收敛时间得到了极大的减少。     

基于全变分去噪的MRI截断伪影抑制方法的研究

截断伪影(又称Gibbs伪影)是MRI常见伪影之一。其产生的原因是K空间的有限采样或者高频数据丢失。基于全变分TV(total variation)的方法来抑制截断伪影。首先把问题转变成求全变分最小值,然后用非线性最优化算法来求解。该算法有良好的边缘保留特性,同时也会导致图像分辨率的下降。在全变分基础上使用拉普拉斯锐化滤波器,实验结果表明该算法可以在保留边界的同时明显提高图像分辨率。     

基于混合变分模型的图像去噪

为了有效抑制噪声,获得更好的视觉效果,提出了一种基于混合变分模型的图像去噪方法。将调和模型和全变分模型进行融合,增强模型的去噪性能,根据自适应选取组合系数,组合系数较大时偏向于全变分模型,较小时偏向于调和模型,这样不仅可以有效去除阶梯效应,同时保护边缘细节,采用仿真对比实验以测试模型性能。结果表明,相对其他去噪模型,相同条件下,该模型取得更优的去噪声效果,提高了图像的质量。     

基于梯度自适应函数的彩色图像变分去噪方法

分析了彩色图像的全变分降噪模型,该模型在降噪的同时可以保持好图像的特征信息,但对于噪声较大的图像具有明显的"阶梯效应".Blomgren的基于梯度自适应函数的去噪模型只能处理灰度图像,因此提出改进的基于彩色图像的梯度自适应函数去噪模型.实验证明,改进的模型有效地解决了"阶梯效应"的发生,提高了模型的去噪能力和边缘保持能力.     

数字图像自适应去噪算法的FPGA实现

针对数字图像中椒盐噪声的滤除,提出一种适合FPGA实现的自适应去噪算法。在传统算法中加入二次噪声检测,并且在DE2平台上搭建数字图像的椒盐噪声自适应去噪验证平台进行验证。     

Iterative Total Variation Regularization with Non-Quadratic Fidelity

A generalized iterative regularization procedure based on the total variation penalization is introduced for image denoising models with non-quadratic convex fidelity terms. By using a suitable sequence of penalty parameters we solve the issue of solvability of minimization problems arising in each step of the iterative procedure, which has been encountered in a recently developed iterative total variation procedure Furthermore, we obtain rigorous convergence results for exact and noisy data. We test the behaviour of the algorithm on real images in several numerical experiments using L ¹ and L ² fitting terms. Moreover, we compare the results with other state-of-the art multiscale techniques for total variation based image restoration. Lin He received the B.S. degree in pure mathematics from Peking University, China in 1997 and the M.A. degree in mathematics from UCLA in 2003. She will complete her Ph.D. degree in mathematics in June 2006 from UCLA. Lin He has been working on PDE and/or wavelet based inverse problems and image processing as well as level set methods and its applications on material sciences. Martin Burger received his master (1998) and PhD (2000) from Johannes Kepler University, Linz, Austria. After working at the Universities of Milano, Linz, and UCLA, he is currently assistant professor at Johannes Kepler University and scientific advisor at the Johann Radon Institute for Computational and Applied Mathematics (RICAM, Austrian Academy of Sciences). Dr. Burger has been working on the numerical solution and applications of inverse problems, mathematical imaging, as well as on the modelling and simulation of problems in materials and life sciences. Stanley Osher received his MS and PhD (1966) from the Courant Institute, NYU. After working at Brookhaven National Laboratory, UC Berkeley and SUNY Stony Brook, he has been at UCLA since 1976. He is Director of Special Projects at the Institute for Pure and Applied Mathematics at UCLA. Dr. Osher is the coinventor of (i) level set methods for computing moving fronts (160,000 references on GOOGLE), (ii) ENO, WENO and other numerical methods for computing solutions to hyperbolic conservation laws and Hamilton-Jacobi equations, (iii) total variation and other PDE based image processing techniques. He has been a Fulbright and Alfred P. Sloan Fellow, received the NASA Public Service Group Achievment Award, Japan Society of Mechanical Engineers Computational Mechanics Award, was an invited speaker at the International Congress of Mathematicians, received the SIAM Pioneer Prize at the last ICIAM conference, the SIAM Kleinman Prize at the last SIAM national meeting and was just (May, 2005) elected to the US National Academy of Sciences. He has cofounded 3 successful companies, based, in part, on his own research. His work has been written up numerous times in the scientific and international media, e.g., Science News, Die Zeit. He is a highly cited researcher, according to web-of-science and is the Associate Editor of a number of major journals.     

基于二阶广义全变差正则项的模糊图像恢复算法

针对图像去模糊问题, 采用二阶广义全变差作为修复图像的正则项构建恢复模型, 并针对重建模型的高阶与非光滑特性, 给出了基于分裂Bregman 迭代的快速算法. 实验结果表明, 该模型和数值算法能够较好地恢复被噪声和模糊污染的图像, 同时可以很好地保留图像的纹理和细节信息.     

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。     

自适应全变分图像去噪模型及其快速求解*

在联合冲击滤波器和非线性各向异性扩散滤波器对含噪图像做预处理的基础上,利用边缘检测算子选取自适应参数,构建能同时兼顾图像平滑去噪与边缘保留的自适应全变分模型,并基于Bregman迭代正则化方法设计了其快速迭代求解算法.实验结果表明,自适应去噪模型及其求解算法在快速去除噪声的同时保留了图像的边缘轮廓和纹理等细节信息,得到的复原图像在客观评价标准和主观视觉效果方面均有所提高.     

基于各向异性全变分的迭代滤波算法

空间邻近度和像素值相似度的双边滤波(BF)器在滤波时,由于其值域滤波核系数的计 算易受到噪声的干扰,在噪声水平较大时,直接使用噪声图像来指导核函数权值计算的方案不可行。 为此,提出一种结合各向异性全变分和BF 的图像去噪算法,将各向异性全变分算法与BF 算法相结 合,首先利用各向异性全变分算法对噪声图像进行处理,得到一幅边缘结构信息较为丰富的结果图 像,接着将该结果图像作为BF 算法的引导图像来指导值域滤波核系数的计算,为保证算法的稳定 性,对上述过程进行迭代处理。此外,为提高各向异性全变分算法的计算效率,引入了Split Bregman 迭代算法进行加速处理。实验表明,该算法能在较好去噪的同时,保留较多的边缘结构信息。     

Inverse Scale Spaces for Nonlinear Regularization

Error minimization of global functionals provides a natural setting for analyzing image processing and regularization. This approach leads to scale spaces, which in the continuous formulation are the solution of nonlinear partial differential equations. In this work we derive properties for a class of inverse scale space methods. The main contribution of this paper is the development of a proof that the methods considered are convergent for convex regularization operators. The proof is based on energy methods and the Bregman distance. Further, estimates for convergence toward a clean image with noisy forcing data is provided in terms of both the L ₂ norm and Bregman distances. This leads to natural estimates of optimal stopping scale for the inverse scale space method. These analytical results are discussed in the context of a numerical example. Johan Lie received his Cand. Scient. (M.S.) degree from the University of Bergen in 2003. He is currently pursuing his PhD degree in applied mathematics within the topic of Diffusion Tensor Imaging of the human brain. His main research interest is image processing using partial differential equations and transform based methods. Jan M. Nordbotten received his Cand. Scient. (M.S.) and Dr. Scient. (Ph.D.) degrees from the University of Bergen in 2002 and 2004, respectively. For his work in his doctorate degree, he was awarded the Lauritz Meltzer award for young scientists. In 2004 and 2005 Nordbotten spent time as a Post. Doc. at Princeton University and the University of Bergen before taking an Associate Professor position in the Department of Mathematics at the University of Bergen in 2006. His main research focus lies in the analysis of partial differential equations arising in the environmental sciences, in particular multi-phase flow in porous media and eco-hydrology.     

图像平滑的自适应保真全变分模型

提出一种自适应保真的全变分平滑模型,证明其解的稳定性。结合各向同性和全变分的优点,利用扩散系数构造保真项,从而增强图像边缘,该模型根据图像的梯度信息确定门限值进而选择合适的图像平滑方法。在去除噪声和保持边缘的同时避免了“阶梯”效应,实验结果表明,该模型能有效地去除噪声,提高图像的峰值信噪比。     

一种改进的双项自适应总体变差去噪模型

研究经典总体变差去噪模型及其改进的自适应去噪模型,提出一种基于预处理图像局部信息的双项自适应模型。利用空间自适应保真项缓解二阶非线性滤波对细节的过度平滑,通过自适应正则化项减少阶梯效应,使数值更稳定和收敛。实验结果表明,与原方法相比,改进方法具有更好的鲁棒性,在噪声较高的情况下仍能取得较好的去噪效果。     

基于整体变分正则的图像盲恢复研究

实现了一种基于TV正则化的图像盲恢复算法。采用了交替迭代算法,保证迭代中能同时恢复出图像以及点扩张函数,并在每步迭代中自适应调整其扩散参数。实验结果也显示了迭代过程的收敛以及鲁棒性(特别是对于非连续的模糊),而且图像和点扩张函数可以在很高的噪声级下恢复。