高阶各向异性扩散小波收缩图像降噪算法

证明一种高阶各向异性扩散与小波收缩的等价性,并根据等价性利用高阶各向异性扩散与小波收缩的优势,提出高阶各向异性扩散小波收缩降噪算法。该算法在低频部分采用经典的非线性扩散方法进行扩散,在高频部分采用高阶各向异性扩散方法进行小波收缩。实验结果表明,高阶各向异性扩散小波收缩算法的计算复杂性介于高阶各向异性扩散与小波收缩算法之间,降噪能力高于这2种方法。     

各向异性小波收缩用于图像分割

已经证明2维情况下一般各向异性扩散与HAAR小波收缩在一定条件下是等价的,基于此等价性的各向异性小波收缩结合了小波收缩与各向异性扩散两种方法的优势。将各向异性小波收缩用于多尺度图像分割,提出一种对多尺度各向异性扩散分割方法的改进方法——多尺度各向异性小波收缩图像分割算法。该算法利用各向异性小波收缩对图像中像素灰度值进行扩散,在尽可能保持边缘的情况下,使同质区域内相邻像素灰度随尺度数增加趋于相同,构造基于尺度的空间栈,从而完成对目标的分割,是一种非监督图像分割方法。对比实验结果表明,该算法在有效处理区域内部不一致性的同时,能够准确地定位目标边缘,实现同质区域的融合,完成分割任务,且该算法收敛速度高于多尺度各向异性扩散分割方法。     

基于小波和四阶各向异性扩散的MLEM低剂量CT重建算法

在低剂量计算机断层扫描CT(computed tomography)重建算法中,传统的最大似然期望最大MLEM(Maximum Likelihood Expectation Maximization)算法随着迭代次数的增加会出现棋盘效应而不能有效地抑制噪声。针对上述问题提出一种基于小波收缩和四阶各向异性扩散相结合的MLEM低剂量CT重建算法。该算法结合小波收缩和各向异性扩散的优点,在每次迭代中,对MLEM重建算法处理后的图像进行离散平稳小波分解,在小波域的高频部分进行小波收缩,低频部分使用降噪效果优质的四阶各向异性扩散进行消噪,最后残留的脉冲噪声点通过中值滤波器进行处理,从而进一步优化图像。仿真实验结果表明,该算法可以有效地去除低剂量CT图像的噪声,且在保持图像边缘和细节信息方面有很好的表现,从而获得高抗噪性能的图像。     

用小波系数估计图像边缘方向的相干增强扩散图像降噪算法

在分析相干增强扩散方法和小波阈值收缩方法之间关系的基础上,给出了相干增强扩散在小波分析意义下的解释,同时解释了相干增强扩散方法与小波阈值收缩方法在图像性质上的等价性。针对相干增强扩散计算扩散矩阵较慢的缺点,提出了一种用小波系数估计图像边缘方向的相干增强扩散图像降噪算法。仿真试验结果表明,该扩散算子可以很好地定位图像边缘,较好地运用了小波的时频分析功能。     

同向平均梯度的各向异性扩散模型

遥感图像成像过程中经常会产生包括高斯噪声和椒盐噪声的图像噪声,这些噪声在很大程度上降低了图像的清晰度,影响了图像的实际应用。如何在有效的去除图像噪声的同时又能够很好的保留图像的纹理信息,成为遥感图像去噪追求的目标。针对林石算子和基于非线性小波阈值的各向异性扩散方程存在的不足,提出一种基于同向平均梯度值的各向异性扩散去噪模型,该模型克服了林石算子和基于非线性小波阈值的各向异性扩散方程无法去除强高斯噪声和椒盐噪声的不足,在有效去除遥感图像噪声的同时,很好的保持了图像的边缘和纹理信息。实验结果表明,提出模型的稳定性和有效性,并且去噪后的图像信噪比较林石算子和基于非线性小波阈值的各向异性扩散方程分别提高了24 dB。     

一种高斯曲率策动和高阶微分相融合的去噪方法

Lee Suk-Ho和Seo Jin Keun提出的基于高斯曲率的去噪方法在处理低梯度区域时,虽然对于保留图像的细节特征非常有效,但是步长选择稍大时,会产生黑白点,过小又会增加迭代次数。针对此问题,提出了一种用Tukeys biweight 函数来控制曲率扩散的修正模型,该模型可以在较大时间步长的情况下避免黑白点的出现。进一步,为了利用高阶去噪方法对高梯度区域进行快速去噪,提出了一种将高斯曲率去噪方程和四阶偏微分方程相融合的去噪模型,以便可以根据具体的图像合理地分配两部分的权重。数值实验证明,该模型不仅可以处理曲面拟合方法所不能消除的椒盐噪声,而且可以实现两种方法的优点互补,既能保持边界,又较好地保留了细节特征。     

基于异性扩散方法的数字图像水印研究

基于人类视觉系统的特性,提出一种结合各向异性扩散和小波域的数字水印算法。根据各向异性扩散在图像处理中具有良好的边缘保持与增强的作用,首先对原图像进行各向异性扩散,在其小波分解高频区域求解噪声敏感模型,确定水印嵌入合适位置,最后把水印信息嵌入到原图像的小波域的等同位置。实验证明了算法在保证水印不可见性的同时,具有较好的鲁棒性。运用各向异性扩散方法的结果也提高了水印方法的安全性。     

一种基于各向异性扩散方程的自适应去噪方法

提出了一种基于各向异性扩散方程的图像自适应去噪方法。分析了各向异性扩散方程在图像除噪中的实现原理,将一种改进的图像结构相似度算法与各向异性扩散方程相结合,实现了对图像的自适应滤波。实验结果表明,改进的结构相似度算法在自适应滤波的应用中有一定的优越性和较好的鲁棒性。     

小波域中的PDE指纹图像增强

提出了一种基于偏微分方程的小波域指纹增强算法。分析了一致性扩散方程的缺陷,改为使用方向扩散使方程严格沿着指纹纹路扩散;进而提出了一种基于方向扩散的小波域指纹增强算法。该算法利用小波域低频系数图增强指纹,抑制了噪声的影响,将增强子图利用小波逆变换实现重构。通过对FVC2002的dB4指纹库中部分低质量图像的增强结果比较,表明该算法对低质量指纹图像的增强效果明显,且处理速度比现存的基于PDE的增强方法快。     

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.     

BDDC preconditioning for high-order Galerkin Least-Squares methods using inexact solvers

A high-order Galerkin Least-Squares (GLS) finite element discretization is combined with a Balancing Domain Decomposition by Constraints (BDDC) preconditioner and inexact local solvers to provide an efficient solution technique for large-scale, convection-dominated problems. The algorithm is applied to the linear system arising from the discretization of the two-dimensional advection–diffusion equation and Euler equations for compressible, inviscid flow. A Robin–Robin interface condition is extended to the Euler equations using entropy-symmetrized variables. The BDDC method maintains scalability for the high-order discretization of the diffusion-dominated flows, and achieves low iteration count in the advection-dominated regime. The BDDC method based on inexact local solvers with incomplete factorization and p = 1 coarse correction maintains the performance of the exact counterpart for the wide range of the Peclet numbers considered while at significantly reduced memory and computational costs.     

High-Order Mixed Current Basis Functions for Electromagnetic Scattering of Curved Surfaces

We construct high-order mixed current vector basis (unctions on an arbitrary curved surface which can be subdivided as a union of curved triangles and quadrilaterals. The objective is to construct vector basis (a) which consists of high-order polynomials of the surface parameterization variables on triangles and quadrilaterals, (b) part of the basis will have vanishing moments on the triangles and quadrilaterals. The first property will enable us to represent the current distribution over scatter surface with much less number of unknowns and larger patches of either triangular or quadrilateral shapes. The second property will achieve what wavelet basis does on an interval, but on a more general domain, namely, a sparse matrix representation for some integral operators.     

Automated low-order to high-order mesh conversion

An algorithm is presented for the CAD-free conversion of linear unstructured meshes into curved high-order meshes, which are necessary for high-order flow simulations. The algorithm operates via three steps: (1) autonomous detection of feature curves along the mesh surface, (2) reconstruction of the surface curvature from the combination of surface node positions and feature curve positions, and (3) alignment of the mesh interior to the newly curved surface. The algorithm is implemented in our freely available cross-platform graphical software program meshCurve, which transforms existing linear meshes into high-order curved meshes

     

Spectral element spatial discretization error in solving highly anisotropic heat conduction equation

This paper describes a study of the effects of the overall spatial resolution, polynomial degree and computational grid directionality on the accuracy of numerical solutions of a highly anisotropic thermal diffusion equation using the spectral element spatial discretization method. The high-order spectral element macroscopic modeling code SEL/HiFi has been used to explore the parameter space. It is shown that for a given number of spatial degrees of freedom, increasing polynomial degree while reducing the number of elements results in exponential reduction of the numerical error. The alignment of the grid with the direction of anisotropy is shown to further improve the accuracy of the solution. These effects are qualitatively explained and numerically quantified in 2- and 3-dimensional calculations with straight and curved anisotropy.     

基于几何特征的曲面物体识别

基于几何特征的曲面物体识别方法是通过从景物深度图象上提取景物表面的高斯曲率和平均曲率、曲率直方图,曲率的熵等几何信息,将景物用一个属性关系图ＡＲＧ来表示,并与模型库中的模型ＡＲＧ图进行优化匹配,从而来识别曲面景物。该方法主要是针对机器零部件等人造曲面物体的识别问题而设计的,其曲面几何特征的描述方法对二阶曲面比较有效,实验表明,应用该方法可成功地从深度图象中识别机器零部件等曲面物体,且有较好的识别结     

Algorithm of gaussian sum filter based on high-order UKF for dynamic state estimation

In this work we consider the state estimation problem in nonlinear/non-Gaussian systems. A new version of Gaussian sum estimation algorithm is developed here based on high-order unscented Kalman filter (HUKF). A sigma point selection method, high-order unscented transformation (HUT) technique is proposed for the HUKF, which can approximate the Gaussian distributions more accurately. We present the systematic formulation of Gaussian filters and develop efficient and accurate numerical integration of the optimal filter. We then go on to extend the use of the HUKF to discrete-time, nonlinear systems with additive, possibly non-Gaussian noise. The resulting filtering algorithm, called the Gaussian sum high-order unscented Kalman filter (GS-HUKF) approximates the predicted and posterior densities as a finite number of weighted sums of Gaussian densities. It is corroborated in the theoretical analysis and the simulation that the proposed Gaussian sum HUKF has integrated advantages with respect to computational accuracy and time complexity for nonlinear non-Gaussian filtering problems.     

Masonry and monolithic circular arches strengthened with composite materials – A finite element model

A finite element model for the stress analysis of circular arches strengthened with composite materials is developed. The formulation uses the principle of virtual work, the Bernoulli–Euler curved beam theory for the arch and the composite reinforcement, and a high-order kinematic assumption that satisfies the compatibility and (with the constitutive laws) the tangential equilibrium conditions of the adhesive. The character of the masonry arch is introduced through the constitutive equations with a distinction between the masonry units and the mortar joints. Convergence and numerical studies that support using high-order shape functions and examine the capabilities of the model are presented.     

基于曲线坐标系下扩散方程的形态学开.闭运算

形态学开、闭运算以腐蚀和膨胀为基础。图像的腐蚀和膨胀统一为笛卡尔直角坐标系下几何制约扩散方程对图像灰度等值线的演化。针对许多曲面上图像，比如柱面帖图，球面帖图，结合深度信息采用曲线坐标系下的几何制约扩散方程(曲面上曲线的演化)来进行形态学运算是一种新的尝试，从结果可以看到处理效果明显优于普通的方法。     

基于四阶偏微分方程的光滑曲面重构方法

常用的基于散点的曲面重构方法如克里金插值法、样条曲面拟合法等存在计算量大、重构曲面不光滑或无法插值已知散点等问题。为此,提出一种基于四阶偏微分方程的曲面重构方法。该方法首先选择一个四阶偏微分方程,并对其构建差分格式,进而分析该差分格式的稳定性和收敛性。在稳定性和收敛性条件下,采用演化的思想,通过有限差分法迭代求解偏微分方程的数值解,并将其稳态解作为原始曲面的逼近。以地质勘探中实际测井数据为例,采用偏微分方程曲面造型方法重构地质曲面,结果表明,该方法计算简便,构造的曲面具有自然光顺性且可以插值于已知散点。     

基于高斯曲率和局部方差的去噪模型

用PM(Perona and Malik)模型去除椒盐噪声,使低噪声强度下未受噪的平坦区域的像素值减小,但是不能在有效去噪的同时保护纹理细节,导致图像模糊.为此,用局部方差和高斯曲率代替梯度模值来描述图像局部纹理细节,并定义了噪声度量函数,随之引入扩散方程,得到新去噪模型.实验结果表明:新模型不仅能有效地除去椒盐噪声和解决PM模型的问题,而且信噪比和峰值信噪比均有显著提高.因此新模型优于PM模型.