含Laplace-Gauss型混合噪声图像二阶正则化重建方法（英文）

假设观测数据含Laplace-Gauss型混合噪声条件下,提出求解数据重建反问题的一种新型一阶二阶混合正则化模型,阐述该模型在断层重建和流体动力学实验定量诊断中的应用.建模过程采用贝叶斯推断理论和期望极大方法,将空间自适应函数引入经典的增广拉格朗日方法得到模型数值算法.所提出的模型及其算法进行图像复原和客体重建实验.结果表明模型算法的可靠性.     

A Regularization Homotopy Strategy for the Constrained Parameter Inversion of Partial Differential Equations

The main difficulty posed by the parameter inversion of partial differential equations lies in the presence of numerous local minima in the cost function. Inversion fails to converge to the global minimum point unless the initial estimate is close to the exact solution. Constraints can improve the convergence of the method, but ordinary iterative methods will still become trapped in local minima if the initial guess is far away from the exact solution. In order to overcome this drawback fully, this paper designs a homotopy strategy that makes natural use of constraints. Furthermore, due to the ill-posedness of inverse problem, the standard Tikhonov regularization is incorporated. The efficiency of the method is illustrated by solving the coefficient inversion of the saturation equation in the two-phase porous media.     

光偏折层析的Tikhonov正则化重建技术

从不适定问题的求解思想出发,建立了使用Tikhonov正则化方法计算流场参量分布的光偏折层析重建技术。理论上详细讨论了偏折信息的转化、投影方程组的正则化、以及由共轭梯度法实现求解等三个主要步骤。用数值模拟考察该方法对非对称温度分布的重建效果,分别计算了对应不同采样数的欠定与超定投影方程组。结果表明,10次迭代后重建分布的平均误差和峰值误差分别为2.1%和5.2%。使用正则化方法对采集的多方向叠栅偏折投影进行计算,重建出双峰温度场。结果表明,使用正则化方法的双峰值相对误差略高,迭代次数减少,可提高重建效率。     

Existence and Completeness of the Wave Operators for Higher Order Differential Operators

The aim of the present paper is to study the existence and the completeness of the wave operators for elliptic operators of higher order (Schr?dinger operator) with short-range potential of the form: and other related results by using the trace class method. MSC: 2000 46N50, 47Dxx, 47F05.     

A Laplace Decomposition Method for Nonlinear Partial Differential Equations with Nonlinear Term of Any Order

A Laplace decomposition algorithm is adopted to investigate numerical solutions of a class of nonlinear partial differential equations with nonlinear term of any order, utt ＋ auxx ＋ bu ＋ cup ＋ du^2p-1 = 0, which contains some important equations of mathematical physics. Three distinct initial conditions are constructed and generalized numerical solutions are thereby obtained, including numerical hyperbolic function solutions and doubly periodic ones. Illustrative figures and comparisons between the numerical and exact solutions with different values of p are used to test the efficiency of the proposed method, which shows good results are azhieved.     

三维点云物体频谱获取方法

为了简化三维物体计算全息数据和加快计算时间,提出了一种三维点云物体频谱获取方法.在分析频谱获取方法模型的基础上,由不同视角的投影图像(视图)与对应的平面波因子相乘积分的方法得到了三维点云物体频谱;介绍了视图获取算法,使用Matlab并行计算得到了一个三维‘鸟’的视图序列;根据实际物体频谱分布情况,采用高阶高斯概率分布减少视图获取数量;通过视图序列得到三维物体的频谱,采用傅里叶逆变换得到物空间内一个平面的复振幅分布,将其衍射一段距离,编码为菲涅尔全息,并进行了模拟再现和实验验证.模拟再现和实验结果表明:只需要原总视图的17.75%可以获得高质量的再现效果,验证了频谱获取方法的可行性及视图获取简化模型的正确性.所获取的三维物体频谱可以通过一定方式编码成多种全息进行三维显示,拓宽了该频谱获取方法的应用范围.     

基于节点重构的扩散方程有限体积格式

研究扭曲网格上扩散方程的九点格式.以经典的九点格式为基础,在通量连续条件下,构造出节点未知量一种新的计算方法,进而得到所希望的格式.分析及数值实验表明,在扭曲网格上,该格式对具有连续或间断扩散系数的问题能够保持较高的精度.     

基于物体特征有效提取和离散点三维重建的3D扫描系统原型研究

针对3D扫描技术的近期发展情况,以及市场关于被摄物体特征有效提取的迫切需求,通过系统的对照相机和投影仪测量的方法与计算,利用离散点三维重建算法、标准化算法详细分析了,作为3D扫描原型系统的关键技术,并深入的对三维坐标重复演算的过程,进行了实践研究与计算,论证了基于投影光编码技术的3D扫描仪原型系统,在物体特征有效提取和离散点三维重建中完全可以高效应用;同时,使用焦距标准化运算、逆向倾角变形运算、逆向扭曲变形运算三种方法,综合论述了物体特征有效提取和离散点三维重建过程的相关内容,测试了原型系统对真实文物的扫描情况,展开了该原型系统可应用于不同材料,不同种类物体的扫描,并能有效的进行数字化物体特征识别的研究结论。     

从一幅载频全息图中实现相位重构的新算法

为了实现对单幅载频下涉图进行相位重构.提出了一种避免相位"解包裹"的简易算法.该算法从载频干涉图中解出所求相位的两个偏导数,然后对两个偏导数积分从而得到所求的相位.利用该算法分别对计算机模拟的干涉图和实验所得干涉图进行相位重构,重构结果均表明该算法能够很好地从载频干涉图样中实现相化重构.并且由于避免了相位"解包裹"的过程,从而简化了相位重构的流程,同时也避免了由相位解包带来的错误或误差.此外,该方法在重构相位时,对干涉图中强度分布的不均匀性不敏感.     

种基于偏微分方程约束的闪光照相图像重建算法

针对闪光照相图像信噪比低的特点,提出了一种基于偏微分方程基于非线性PDE的约束的图像重建算法,该算法在重建迭代过程中引入了基于非线性PDE的平滑约束来抑制图像噪声,同时保护图像边缘。数值试验结果表明:相比于Landweber和预优约束共轭梯度（PCCG）重建算法,新算法具有更强的抗噪能力和边缘保护能力,是一种更加有效的闪光照相图像重建算法。     

A Unified Lattice Boltzmann Model for Fourth Order Partial Differential Equations with Variable Coefficients

In this work, a unified lattice Boltzmann model is proposed for the fourth order partial differential equation with time-dependent variable coefficients, which has the form ut+α(t)(p1(u))x+β(t)(p2(u))xx+γ(t)(p3(u))xxx+η(t)(p4(u))xxxx=0. A compensation function is added to the evolution equation to recover the macroscopic equation. Applying Chapman-Enskog expansion and the Taylor expansion method, we recover the macroscopic equation correctly. Through analyzing the error, our model reaches second-order accuracy in time. A series of constant-coefficient and variable-coefficient partial differential equations are successfully simulated, which tests the effectiveness and stability of the present model.