图像复原的Contourlet收缩与广义全变分正则化方法

建立了广义全变分(total variation,TV)模型,分析正则项在复原算法中的作用.分别从图像的平坦区域和边缘区域入手,在平坦区域图像各向同性扩散,在边缘区域则要满足各向异性扩散,从理论上对两种情形下的扩散做深入分析,推导出广义TV模型满足的一些条件,为了防止高噪声情形下复原模型失效以及克服方块效应,在正则项中引入了 Contourlet收缩,它是一种多分辨的、局域的、多方向的更稀疏的图像表示方法,正则项中引入的Contourlet收缩具有去噪和提取图像重要信息的作用,Contourlet收缩与广义TV正则化相结合,兼顾了图像的光滑性和边缘保持,特别是在图像严重模糊、噪声越多的情形下,更加体现了这种算法比改进的TV模型有效.     

改进的TV模型图像修复算法

分析了基于整体变分(total variation,TV)模型的图像修复算法,TV模型修复算法只使用各向异性扩散,TV模型各向异性扩散仅向图像边缘方向扩散,容易在平滑区域引入阶梯效应.提出了一种改进的图像修复算法,该算法同时结合了各向同性和各向异性扩散,利用区域频率差异实现了在不同的区域使用不同的迭代方程,有效避免了原始算法引入的阶梯效应,同时在平滑区域提高了迭代效率.Matlab环境下的仿真结果表明,改进算法的修复效果和峰值信噪比的计算结果均明显优于原始算法.     

Augmented Lagrangian Method for Total Variation Based Image Restoration and Segmentation Over Triangulated Surfaces

Recently total variation (TV) regularization has been proven very successful in image restoration and segmentation. In image restoration, TV based models offer a good edge preservation property. In image segmentation, TV (or vectorial TV) helps to obtain convex formulations of the problems and thus provides global minimizations. Due to these advantages, TV based models have been extended to image restoration and data segmentation on manifolds. However, TV based restoration and segmentation models are difficult to solve, due to the nonlinearity and non-differentiability of the TV term. Inspired by the success of operator splitting and the augmented Lagrangian method (ALM) in 2D planar image processing, we extend the method to TV and vectorial TV based image restoration and segmentation on triangulated surfaces, which are widely used in computer graphics and computer vision. In particular, we will focus on the following problems. First, several Hilbert spaces will be given to describe TV and vectorial TV based variational models in the discrete setting. Second, we present ALM applied to TV and vectorial TV image restoration on mesh surfaces, leading to efficient algorithms for both gray and color image restoration. Third, we discuss ALM for vectorial TV based multi-region image segmentation, which also works for both gray and color images. The proposed method benefits from fast solvers for sparse linear systems and closed form solutions to subproblems. Experiments on both gray and color images demonstrate the efficiency of our algorithms.     

优化-最小求解的广义总变分图像复原

在代价函数中嵌入总变分正则项是解决图像复原中不适定问题的一种有效方法。但是,总变分正则化考虑的仅是一阶而不是高阶邻域像素变分关系;另外,总变分的开方形式还给基于总变分代价函数的优化带来了困难。为此,提出一种基于优化-最小算法的广义总变分正则化图像复原新方法,以克服目前存在的问题。该方法保留了总变分正则化方法能够除噪声保边缘的重尾特征,同时借鉴了双边总变分双重加权机制,从而推导出总变分正则项在邻域范围上的推广形式。该方法还针对广义总变分正则项优化过程中存在的求解瓶颈,提出采用优化-最小算法求得上界函数以逐次逼近最优解。实验结果表明,该方法取得了较好的复原效果,使改善信噪比指标达到2dB左右。     

Linearized proximal alternating minimization algorithm for motion deblurring by nonlocal regularization

Non-blind motion deblurring problems are highly ill-posed and so it is quite difficult to find the original sharp and clean image. To handle ill-posedness of the motion deblurring problem, we use nonlocal total variation (abbreviated as TV) regularization approaches. Nonlocal TV can restore periodic textures and local geometric information better than local TV. But, since nonlocal TV requires weighted difference between pixels in the whole image, it demands much more computational resources than local TV. By using the linearization of the fidelity term and the proximal function, our proposed algorithm does not require any inversion of blurring operator and nonlocal operator. Therefore, the proposed algorithm is very efficient for motion deblurring problems. We compare the numerical performance of our proposed algorithm with that of several state-of-the-art algorithms for deblurring problems. Our numerical results show that the proposed method is faster and more robust than state-of-the-art algorithms on motion deblurring problems.     

Image Restoration with Discrete Constrained Total Variation Part II: Levelable Functions, Convex Priors and Non-Convex Cases

In Part II of this paper we extend the results obtained in Part I for total variation minimization in image restoration towards the following directions: first we investigate the decomposability property of energies on levels, which leads us to introduce the concept of levelable regularization functions (which TV is the paradigm of). We show that convex levelable posterior energies can be minimized exactly using the level-independant cut optimization scheme seen in Part I. Next we extend this graph cut scheme to the case of non-convex levelable energies.We present convincing restoration results for images corrupted with impulsive noise. We also provide a minimum-cost based algorithm which computes a global minimizer for Markov Random Field with convex priors. Last we show that non-levelable models with convex local conditional posterior energies such as the class of generalized Gaussian models can be exactly minimized with a generalized coupled Simulated Annealing.     

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。     

基于张量总变分的模糊图像盲复原

现有模糊图像盲复原算法通常仅利用彩色图像的灰度信息估计模糊核,彩色图像转换成灰度图像的操作会造成信息丢失,在处理尺寸过小或显著边缘过少的图像时,模糊核的估计通常会失效,导致最后复原图像的质量不理想。针对上述问题,在新的张量框架下,把彩色模糊图像作为一个三阶张量,提出了一种基于张量总变分的模糊图像盲复原算法。首先通过调整张量总变分模型中的正则化参数获取彩色图像不同尺度的边缘信息,从而估计出模糊核;再利用张量总变分算法对模糊图像解模糊,复原出清晰图像。实验结果表明,所提算法得到的复原图像在峰值信噪比（PSNR）和主观视觉上均得到明显改善。     

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。     

基于张量奇异值分解的动态核磁共振图像重建

本文为了改善动态MR图像重建质量,提出了一种结合张量奇异值分解和全变分稀疏模型(TV)的动态核磁共振图像重建算法。算法对动态MR图像进行了低秩约束规范和稀疏约束规范,分别使用了张量奇异值分解阈值方法和全变分稀疏变化基方法求解。实验结果和重建视觉效果表明,在相同采样率下本文算法与单独使用全变分方法,k-t SLR方法,单独使用张量奇异值分解方法相比重建质量更优,在峰值信噪比(PSNR),均方差(MSE)和结构相似性度量(SSIM)的评价指标上有所提高,对图像去噪去模糊重建有具体的应用价值。     

基于变分法和偏微分方程的图像彩色化方法

针对传统的图像彩色化算法易产生的图像边缘颜色模糊等问题,提出一种基于变分法和偏微分方程的图像彩色化算法,结合整体变分(TV)模型和金兹堡一朗道(GL)模型的特点,通过求泛函极值建立偏微分方程,使图像的光滑区域和边界区域都能有效的实现颜色扩散,对偏微分方程进行数值求解得到彩色化结果.实验结果表明,与其它偏微分方程彩色化技术相比,该方法能得到清晰自然的彩色化图像和较高的图像质量.     

一种改进的各向异性全变差去噪模型

全变差（TV）正则化模型是最经典的去噪模型,利用分裂的Bregman迭代算法可以简单有效地求解该模型。结合TV-L1模型和OSV模型,提出了一种改进的各向异性全变差去噪模型,并且利用分裂的Bregman迭代算法进行求解。通过数值实验可以看出改进的模型保护了恢复图像的边缘,突出了几何特征和纹理,使其更加清晰,去噪效果比原模型有所提高。     

A fast higher degree total variation minimization method for image restoration

Based on the spectral decomposition theory, this paper presents a unified analysis of higher degree total variation (HDTV) model for image restoration. Under this framework, HDTV is reinterpreted as a family of weighted L₁–L₂ mixed norms of image derivatives. Due to the equivalent formulation of HDTV, we construct a modified functional for HDTV-based image restoration. Then, the minimization of the modified functional can be decoupled into two separate sub-problems, which correspond to the deblurring and denoising. Thus, we design a fast and efficient image restoration algorithm using an iterative Wiener deconvolution with fast projected gradient denoising (IWD-FPGD) scheme. Moreover, we show the convergence of the proposed IWD-FPGD algorithm for the special case of second-degree total variation. Finally, the systematic performance comparisons of the proposed IWD-FPGD algorithm demonstrate the effectiveness in terms of peak signal-to-noise ratio, structural similarity and convergence rate.     

全变差图像恢复的交替方向乘子法

针对图像恢复的全变差（TV）模型提出了一种基于交替方向乘子法的快速求解算法。通过变量替换将TV模型转化为与之完全等价的等式约束优化问题,然后用交替方向乘子法求解等式约束优化问题。实验结果表明,相对于FTVd方法,克服了FTVd方法的不稳定性,视觉效果更好,信噪比也得到了提高。     

Image Restoration with Discrete Constrained Total Variation Part I: Fast and Exact Optimization

This paper deals with the total variation minimization problem in image restoration for convex data fidelity functionals. We propose a new and fast algorithm which computes an exact solution in the discrete framework. Our method relies on the decomposition of an image into its level sets. It maps the original problems into independent binary Markov Random Field optimization problems at each level. Exact solutions of these binary problems are found thanks to minimum cost cut techniques in graphs. These binary solutions are proved to be monotone increasing with levels and yield thus an exact solution of the discrete original problem. Furthermore we show that minimization of total variation under L ¹ data fidelity term yields a self-dual contrast invariant filter. Finally we present some results.     

消除halo效应和色彩失真的去雾算法

目的 雾天条件下采集的图像存在低对比度和低场景可见度的问题,传统的去雾算法易产生halo效应和色彩失真问题。为此,结合大气散射光特性提出一种基于相对总变差的图像复原方法。方法 首先从大气散射光与纹理信息无关的角度出发,利用相对总变差分离图像主结构和图像纹理信息准确估计大气耗散函数,通过引入一个自适应保护因子来避免复原图像的色彩失真问题,最后由大气散射模型计算复原图像并进行图像的亮度调整,得到一幅清晰无雾的图像。结果 通过与经典的去雾算法比较,表明该方法可以有效避免halo效应和天空颜色失真等不足,并且在图像的深度突变处也能得到很好的去雾效果。结论 实验表明该算法的场景适应能力较强,时间复杂度与图像的大小成线性关系,相比于前人的算法在计算速度上有一定的提高。     

多网格法解总变分问题及在医学图像增强中的应用

传统的各向同性平滑方法，如拉普拉斯平滑方法，虽然能去掉图像的噪声，但同时也可能使图像的边缘信息模糊，甚至丢失。针对这种情况，基于总变分的平滑方法得到重视，因为该方法可以在去除噪声的同时，对边缘的信息进行增强，但是由于基于总变分的平滑方法计算量大，且用松弛法迭代的收敛速度比较慢，因此引入了多网格预处理的共轭梯度算法来解总变分问题。计算结果表明，共轭梯度法的收敛速度明显高于松弛法，而采用多网格法收敛速度还可以得到进一步提高。为说明该方法的优点，最后对用这两种方法处理的超声医学图像的收敛曲线和平滑结果进行了比较。     

倒谱和快速全变差去卷积的运动模糊图像复原

物体和成像系统之间的相对运动导致图像产生运动模糊,降低了图像质量,为了获得更加理想的复原图像,提出一种基于倒谱和快速全变差去卷积相结合的运动模糊图像复原算法。利用倒谱法对运动模糊图像的点扩散函数参数（模糊角度和模糊尺度）进行辩识,采用快速全变差去卷积法对模糊图像进行复原,采用多幅图像进行仿真实验测试算法的性能。仿真结果表明,相对于经典图像复原算法,该算法复原图像的主观视觉效果以及客观评价指标均更优,具有一定的实际利用价值。     

基于交叠组合稀疏高阶全变分的图像复原

针对传统全变分进行扩展,提出了一种高阶全变分结合交叠组合稀疏的新算法,将像素级别梯度信息推广为高阶交叠组合稀疏梯度信息,更好地抑制了因全变分产生的阶梯效应并保存了图像边缘等细节信息。为了解决提出的图像复原新算法的优化问题,采用交替方向乘子算法（ADMM）来交替求解优化问题。将提出的新算法与其他几种相关算法相比,并用峰值信噪比（PSNR）和结构相似性（SSIM）两个评价指标来评价图像复原后的质量,从而论证了新算法的优越性。     

二阶总广义变分小波修复模型

目的 针对全变分小波修复模型易导致阶梯效应的缺陷,提出一种加权的二阶总广义变分小波修复模型。方法 不同于全变分小波修复模型,假设的新模型引入二阶导数项且能够自动地调解一阶和二阶导数项。另外,为有效地利用图像的局部结构信息,新模型引入了权函数,它既能保护图像的边缘又增强光滑区域的去噪能力。 为有效地计算新模型,利用交替方向法将该模型变为两个子模型, 然后对两个子模型分别给出相应的理论和算法推导。结果 相比最近基于全变分正则小波修复模型(平均信噪比,平均绝对误差及平均结构相似性指标分别为21.884 4,6.857 8,0.827 2),新模型得到更好的修复效果(平均信噪比,平均绝对误差及平均结构相似性指标分别为22.313 8,6.626 1,0.831 8)。结论 与全变分正则相比,二阶总广义变分正则更好地减轻阶梯效应。目前, 国内外学者对该问题的研究取得一些结果。由于原始-对偶算法需要较小的参数,所以运算的速度较慢,因此更快速的算法理论有待进一步研究。另外,该正则能应用于图像去噪、分割、放大等方面。