小波构造变正则参数变分模型在带噪图像恢复中的应用

在利用正则化方法构造变分模型进行图像去噪时，其正则参数往往选择为恒定值．文中利用小波分解的层次性和带噪图像中噪声所具有的时频特点，构造出变正则参数的变分模型．在不同的小波分解层，通过选择不同的正则参数从而达到自适应去噪的目的．     

基于正则化的多光谱图像二值化处理

为了进一步提升传统多光谱图像二值化处理方法的处理速度和抗噪性能,提出基于正则化的多光谱图像二值化处理方法。将正则化约束引入到多光谱图像去噪模型中,对现有的多光谱去噪模型进行改进。并利用正则化框架中的数据正则项对图像的噪声机制以及图像的先验信息进行建模,以实现多光谱图像去噪处理。根据去噪结果采用约束能量最小化方法获取多光谱图像的边缘信息,将最佳全局阈值法和局部阈值自适应方法在边缘信息的基础上相结合,实现对多光谱图像的二值化处理。仿真结果表明,所设计方法具有较强的抗噪能力和较快的处理速度,并且经处理后的图像分辨率较高,充分验证了上述方法的有效性。     

Tikhonov正则化方法在带噪数字图像缩放中的应用

利用正则化方法对带噪声图像的缩放问题进行了讨论，提出带噪图像缩放的变分模型，并利用样条构造出变分模型的解。该方法使得带噪图像在进行缩放时噪声的影响得到了较好抑制，通过选择不同的正则参数，可以得到不同效果的缩放结果。     

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。     

一种结合小波阈值滤波的自适应整体变分方法

在整体变分方法去噪原理的基础上,通过引入小波阈值滤波,用自适应正则项代替整体变分模型中的正则项,提出了一种依赖于信号的局部信息进行滤波的自适应整体变分方法,自适应地在整体变分正则化和各向同性光滑化之间调整滤波强度。为求解整体变分极小化问题,采用了滞后扩散定点迭代的方法。数值计算结果表明：提出的方法有效地减少了传统整体变分方法去噪后恢复信号中所出现的阶梯效应,很好地抑制了小波变换中固有的伪Gibbs现象,重构信号的边缘、不连续点位置十分精确,信噪比也得到明显改善。     

Besov空间下迭代全变差正则化的图像恢复模型

在Besov空间下,提出了一种用于图像恢复领域的迭代全变差正则化模型。通过使用一个加权的参数序列,给出了一个迭代正则化的变分问题,这个变分问题实际上是一个小波软硬阈值结合的迭代程序。给出了新模型的停止标准和一些好的性质,如单调性和收敛性等。数值实验表明与传统去噪方法相比,新方法不仅能较好地恢复图像,而且收敛速度较快。     

一种基于非抽样LP的Contourlet变换图像去噪方法

由于提高Contourlet变换冗余性可以抑制去噪结果中的伪Gibbs现象,因此为了提高变换冗余度和避免数据量过大,以进行快速有效的图像去噪,提出了一种基于非抽样LP的Contourlet变换图像去噪方法。该方法首先对带噪图像进行非抽样LP多尺度分解;然后对各子带图像进行临界抽样的DFB分解,再采用尺度相关的分层模型对各子带图像进行阈值处理;最后对处理后的子带图像进行DFB和LP重建,以得到去噪后的图像。与同类型有关方法进行的对比实验表明,在去噪后图像的PSNR值上,该方法比常规Contourlet变换方法至少提高1dB;在完成时间方面,该方法比其他改进方法快1倍以上。     

改进小波软阈值函数在图像去噪中的研究应用

常规小波软阈值去噪方法处理前后的图像小波系数有所差异,导致去噪后图像失真严重.为进一步提升去噪效果,提高去噪和细节保持能力,对阈值的选取方式和阈值函数进行改进.改进方法通过小波变换的每一级子带长度确定阈值,实现阈值自适应准确量化,改进软阈值函数采用双曲正切函数替换符号函数,对阈值绝对值范围内的小波系数应用非线性函数进行...     

基于提升小波的自适应阈值图像去噪

介绍了提升方法(Lifting Scheme)的基本原理,给出了用提升方法构造传统小波的实现方法.在提升小波分解变换的基础上,研究一种自适应阈值的图像去噪方法--AdaptThr Shrink去噪法.这种方法是基于Bayes框架,在不同子带和不同方向上选择不同的最佳阐值.结合软阈值法对图像进行去噪,与传统方法相比,此种方法提高了去噪后图像的峰值信噪比(PSNR),而且使图像更加清晰.基于提升小波的自适应阈值图像去噪法实现简单、计算速度快、去噪效果好.     

正则化超分辨率重建过程的自适应阈值去噪

为了提高正则化超分辨率技术在噪声环境下的重建能力,对广义总变分（GTV）正则超分辨率重建进行了扩展研究,提出了一种自适应阈值去噪的方法。首先,根据GTV正则超分辨率重建算法进行迭代重建;然后,利用推导出的自适应阈值矩阵,对每次迭代产生的代价矩阵进行阈值划分,小于阈值的对应像素点继续迭代,大于阈值的对应像素点被截断后重新插值并不再参与本轮迭代;最后,程序达到收敛条件时输出重建结果。实验结果表明,通过与单一GTV正则重建和自适应参数的方法相比,自适应阈值去噪的方法提高了收敛速度和重建图像的质量,使正则化超分辨率技术在噪声环境下有更好的重建能力。     

Besov空间的阈值收缩和边缘补偿的图像去噪

提出一种新的图像去噪方法,它是Besov空间的变分模型,在负实数次Sobolev空间上定义了数据项,用Besov半范数定义了正则项。并详细推导了变分模型在Besov空间的阈值求解公式,先做一个Contourlet变换域的小阈值收缩,然后再利用该模型去噪。去除噪声的同时也损失了部分边缘信息,把边缘分为四种情况,针对不同情况确定相应的边缘补偿方法。实验表明该模型具有良好的去噪效果。     

基于变分模态分解的直肠压力信号预处理研究

针对依托于人工肛门括约肌系统的直肠功能诊断模型中采集信号存在大量干扰噪声的问题,提出了一种基于变分模态分解(VMD)算法与小波加权平均阈值去噪结合的预处理方法。利用VMD算法对原始直肠压力信号进行分解,对各模态分量进行小波阈值去噪,提取出有用信号进行重构。通过仿真比较分析该方法与EMD、小波阈值去噪等方法的去噪效果。实验结果表明,该方法在不同噪声水平下均显著提高输出信号的信噪比,同时避免原始信号中有用信息的丢失,具有良好的去噪效果,对直肠功能诊断的准确性具有重要意义。     

Mesh Denoising using Extended ROF Model with L1 Fidelity

This paper presents a variational algorithm for feature‐preserved mesh denoising. At the heart of the algorithm is a novel variational model composed of three components: fidelity, regularization and fairness, which are specifically designed to have their intuitive roles. In particular, the fidelity is formulated as an L₁ data term, which makes the regularization process be less dependent on the exact value of outliers and noise. The regularization is formulated as the total absolute edge‐lengthed supplementary angle of the dihedral angle, making the model capable of reconstructing meshes with sharp features. In addition, an augmented Lagrange method is provided to efficiently solve the proposed variational model. Compared to the prior art, the new algorithm has crucial advantages in handling large scale noise, noise along random directions, and different kinds of noise, including random impulsive noise, even in the presence of sharp features. Both visual and quantitative evaluation demonstrates the superiority of the new algorithm.     

基于偏微分方程的混合噪声去噪研究

针对目前图像去噪方法存在的主要缺陷是仅适用于单一噪声的滤除, 无法解决图像混合噪声去噪的问题, 提出一种加权混合噪声模型, 建立其能量泛函表达式, 利用变分法获得其欧拉—拉格朗日方程并给出其显式差分迭代求解算法。通过对其数值算法的改进, 不仅提高了该模型数值算法的速度和稳定性, 而且在一定程度上避免了降噪后图像的阶梯效应。仿真实验表明, 加权混合噪声去噪算法在去除混合噪声的同时更好地保留了图像的细节信息, 其降噪性能相比现有方法有一定程度的改善。     

A Framework for Moving Least Squares Method with Total Variation Minimizing Regularization

In this paper, we propose a computational framework to incorporate regularization terms used in regularity based variational methods into least squares based methods. In the regularity based variational approach, the image is a result of the competition between the fidelity term and a regularity term, while in the least squares based approach the image is computed as a minimizer to a constrained least squares problem. The total variation minimizing denoising scheme is an exemplary scheme of the former approach with the total variation term as the regularity term, while the moving least squares method is an exemplary scheme of the latter approach. Both approaches have appeared in the literature of image processing independently. By putting schemes from both approaches into a single framework, the resulting scheme benefits from the advantageous properties of both parties. As an example, in this paper, we propose a new denoising scheme, where the total variation minimizing term is adopted by the moving least squares method. The proposed scheme is based on splitting methods, since they make it possible to express the minimization problem as a linear system. In this paper, we employed the split Bregman scheme for its simplicity. The resulting denoising scheme overcomes the drawbacks of both schemes, i.e., the staircase artifact in the total variation minimizing based denoising and the noisy artifact in the moving least squares based denoising method. The proposed computational framework can be utilized to put various combinations of both approaches with different properties together.     

变正则参数方法在带噪图像保边缘恢复中的应用

提出变正则参数的变分方法．该方法通过选取随梯度变化的自适应的正则参数，达到去噪和保持边缘的目的．通过5点格式构造出变分模型的离散解法，可以避免格林函数的繁琐计算。     

A well-balanced and adaptive variational model for the removal of mixed noise

Image denoising is one of the fundamental problems concerning image processing. Over the last decade mathematical models based on partial differential equations and variational techniques have led to superior results related to denoising problems. The additive noise models have been studied extensively, however, the reconstruction of images corrupted by nonadditive noise has not yet been thoroughly studied. In this paper, a novel variational method for the reconstruction of images corrupted by non-uniformly distributed noise is presented. The proposed model includes a balance between the data term and the regularization term in the energy functional, which takes into account the statistical control of the parameters and the position of the noisy points related to the edges presented in the image. The parameters are determined by the given initial noisy image. The obtained results have shown the effectiveness and robustness of the proposed model and in restoring images with multiplicative noise or mixed Gaussian noise, while preserving edges and small structures belonging to the image.     

Image thresholding by variational minimax optimization

In this paper we introduce an adaptive image thresholding technique via minimax optimization of a novel energy functional that consists of a non-linear convex combination of an edge sensitive data fidelity term and a regularization term. While the proposed data fidelity term requires the threshold surface to intersect the image surface only at places with large image gradient magnitude, the regularization term enforces smoothness in the threshold surface. To the best of our knowledge, all the previously proposed energy functional-based adaptive image thresholding algorithms rely on manually set weighting parameters to achieve a balance between the data fidelity and the regularization terms. In contrast, we use minimax principle to automatically find this weighting parameter value, as well as the threshold surface. Our conscious choice of the energy functional permits a variational formulation within the minimax principle leading to a globally optimum solution. The proposed variational minimax optimization is carried out by an iterative gradient descent with exact line search technique that we experimentally demonstrate to be computationally far more attractive than the Fibonacci search applied to find the minimax solution. Our method shows promising results to preserve edge/texture structures in different benchmark images over other competing methods. We also demonstrate the efficacy of the proposed method for delineating lung boundaries from magnetic resonance imagery (MRI).     

小波域上图像非线性扩散滤波

提出一个小波域上图像扩散滤波恢复新模型。主要思想是把原图像作为最精细尺度下的小波子带，根据噪声分布的特点，导出保护较大尺度下信息的泛函模型代替小波阈值除噪，对泛函求变分得：Euler-Lagrange方程。新的滤波方法能避免小波阈值除噪的伪Gibbs现象，改进了同类型非线性扩散方程滤波的效果。利用可加算子分裂(AOS)格式求非线性扩散方程的数值解。实例的数值计算说明对图像滤波和保护边缘的有效性。