Numerical solution for a class of SPDEs over bounded domains

Parabolic stochastic partial differential Equations (SPDEs) with multiplicative noise play a central rôle in nonlinear filtering. More precisely, the conditional distribution of a partially observed diffusion solves the normalized version of an equation of this type. We show that one can approximate the solution of the SPDE by the (unweighted) empirical measure of a finite system of interacting particle for the case when the diffusion evolves in a compact state space with reflecting boundary. This approximation differs from existing approximations where the particles are weighted and the particle interaction arises through the choice of the weights and not at the level of the particles' motion as it is the case in this work. The system of stochastic differential equations modelling the trajectories of the particles is approximated by the recursive projection scheme introduced by Pettersson [Stoch. Process. Appl. 59(2) (1995), pp. 295–308].     

A representation theory for the impulse control of jump processes

A state space representation theory for the impulse control of a quite general class of non-Markov jump processes is developed. Control decisions are based upon observations of past histories of an input jump process and observations of the current state of the corresponding controlled output. A verification theorem establishes that a solution of a system of quasi variational inequalities gives rise naturally to an optimal impulse policy. The proof of optimality relies upon an extended version of the well-known Dynkin formula for Markov processes.     

An efficient approximation for stochastic differential equations on the partition ofsymmetricalirst

In certain applications of stochastic differential equations a numerical solution must be found corresponding to a particular sample path of the driving process. The order of convergence of approximations based on regular samples of the path is limited, and some approximations are asymptotically efficient in that they minimise the leading coefficient in the expansion of mean-square errors as power series in the sample step size. This paper considers approximations based on irregular samples taken at the passage times of the driving process through a series of thresholds. Such approximations can involve less computation than their regular sample counterparts, particularly for real-time applications. The orders of convergence of the Euler and Milshtein approximations are derived and a new approximation is defined which is asymptotically efficient with respect to the irregular samples. Its asymptotic mean-square error is less than half that of efficient approximations based on regular sample     

Nonlinear filtering of semi-Dirichlet processes

Herein, we consider the nonlinear filtering problem for general right continuous Markov processes, which are assumed to be associated with semi-Dirichlet forms. First, we derive the filtering equations in the semi-Dirichlet form setting. Then, we study the uniqueness of solutions of the filtering equations via the Wiener chaos expansions. Our results on the Wiener chaos expansions for nonlinear filters with possibly unbounded observation functions are novel and have their own interests. Furthermore, we investigate the absolute continuity of the filtering processes with respect to the reference measures and derive the density equations for the filtering processes.     

一种新的方向滤波器组及其在图像去噪中的应用

通过将二维棋盘形滤波器对和二维余弦调制滤波器组相结合,构造了具有方向和频率选择性的新的方向滤波器组。本文中,我们首先设计了具有45度和135度方向的二维棋盘形滤波器对。通过棋盘形滤波器对,输入图像首先被分解为两幅图像。然后,二维余弦调制滤波器组被分别应用到每幅图像。这种结构等效于一个冗余比为2的方向滤波器组。新的滤波器组具有良好的方向和频率选择性。作为新滤波器组的一个应用,我们把双重局部维纳滤波算法和新的方向滤波器组相结合,提出了一种新的图像去噪算法。实验结果表明：对于具有丰富纹理的图像,提出的算法获得了明显的去噪性能改善。     

一种基于特征点跟踪的电子稳像算法

提出一种基于特征点跟踪的稳像算法。该算法从参考帧图像中提取出一组特征点,然后在后续帧中进行基于Kalman滤波的特征点的跟踪,匹配参考帧图像中特征点的坐标和当前图像中基于Kalman滤波修正后得到的特征点的坐标,并通过仿射模型求出位移量及旋转参数,最后进行反向变换,从而得到稳定的视频图像。实验结果表明:该算法稳像效果好,运算复杂度低,且具有较强的鲁棒性。     

基于辅助粒子滤波算法的红外目标跟踪

针对红外目标在跟踪中计算复杂的问题,构建辅助粒子滤波算法。利用贝叶斯重要性采样算法,在权值大的粒子基础上引入辅助粒子变量,然后重新定义重要采样分布函数,防止重采样后粒子概率密度变化。两次加权计算,使粒子权值比仅用重采样的粒子权值变化更稳定,采样点最接近真实状态;同时不同权值粒子的概率阈值可作为粒子滤波是否完成的判断准则。在二维平面构造红外运动目标模型中,系统为零均值高斯白噪声。仿真数据表明:该算法在x,y方向的均方误差、画面处理时间、RM SE性能上优于粒子滤波算法和重采样粒子滤波算法。     

阿贝成像原理和空间滤波实验的改进

改进了阿贝成像原理和空间滤波实验.将物平面置于傅里叶变换透镜的前焦面,采用扩束光照明,在光源的共轭像面上测量频谱分布、改造频谱等,可以获得更好的实验效果,同时简化了光路.     

基于随机共振进行弱信号探测的实验研究

非线性随机共振系统可利用噪声增强微弱信号检测的能力,为强噪声背景下微弱信号的检测开创了新方法.基于随机共振的基本原理设计了硬件电路系统,并将其应用于检测单频和多频微弱信号;通过输入模拟工程实际的带噪信号,采样所得的输出信号的频谱分析结果表明,利用随机共振技术可从强噪声背景下有效地提取出单频和多频弱信号.多频弱信号的有效提取拓展了基于随机共振原理的弱信号检测技术的应用领域,结合数字滤波处理技术有效地消除了低频噪声对信号识别的影响.基于随机共振的弱信号检测技术在信息识别与信息处理方面具有巨大的潜在的应用价值.