Parameter estimation for a morphochemical reaction-diffusion model of electrochemical pattern formation

The process of electrodeposition can be described in terms of a reaction-diffusion partial differential equation (PDE) system that models the dynamics of the morphology profile and the chemical composition. Here we fit such a model to the different patterns present in a range of electrodeposited and electrochemically modified alloys using PDE constrained optimization. Experiments with simulated data show how the parameter space of the model can be divided into zones corresponding to the different physical patterns by examining the structure of an appropriate cost function. We then use real data to demonstrate how numerical optimization of the cost function can allow the model to fit the rich variety of patterns arising in experiments. The computational technique developed provides a potential tool for tuning experimental parameters to produce desired patterns.     

基于NURBS的PDE曲面构造法研究及应用

由非均匀有理Ｂ样条曲线曲面给定边界条件，用偏微分方程来构造曲面，以参数“ａ”控制其整体形状，本文分析其思路原理及过程，并列举了在ＣＡＤ上的应用，最后分析了优缺点。     

变形体温度场和位移场的计算

本文用热源法对简单热传导问题进行了解析解的计算，并应用PDE工具箱求解热传导偏微分方程得到数值解。通过两种温度场的计算结果求出相应的位移场结果，比较可知MATLAB中PDE工具箱对难以用解析法求解的热传导问题有一定的指导作用。     

Averaged control

We analyze the problem of controlling parameter-dependent systems. We introduce the notion of averaged control according to which the quantity of interest is the average of the states with respect to the parameter.First we consider the problem of controllability for linear finite-dimensional systems and show that a necessary and sufficient condition for averaged controllability is an averaged rank condition, in the spirit of the classical rank condition for linear control systems, but involving averaged momenta of any order of the matrices generating the dynamics and representing the control action.We also describe some open problems and directions of possible research, in particular on the average controllability of evolution partial differential equations. In this context we analyze also the averaged version of a classical optimal control problem for a parameter dependent elliptic equation and derive the corresponding optimality system.     

基于偏微分方程的条码预处理

由于受到条码采集设备的限制,图像中经常混有很多噪声,导致出现误码．引入了基于偏微分方程（PDE）的Perona—Malik模型,并对Perona-Malik模型的缺点进行了算法改进,给出了一种针对条码图像去噪的方法．通过合理地设计和选择参数,得到了比较令人满意的结果．     

基于偏微分方程的图像修复技术

介绍了图像修复技术的概念和原理,并在修复方法的理论与技术基础上,深入研究了偏微分方程修复模型中几种具有代表性的BSCB模型、曲率驱动扩散(CDD)模型、TV模型等图像修复模型.最后对上述模型进行了分析比较.     

SAR图像斑点噪声整体变分偏微分方程滤波算法研究

SAR图像固有的斑点噪声严重影响了图像的判读和后续处理,因此抑制SAR图像斑点噪声显得尤其重要。一个良好的斑点噪声抑制算法应该在降低斑点噪声的同时,能很好地保持图像的细节特征,但现有的去噪算法没有一种能够完美地解决这个问题的。本文基于SAR图像斑点噪声滤波的重要性以及存在的问题,将整体变分偏微分方程用于去除斑点噪声。根据整体偏微分方程建立了去噪模型,并分析了模型的性能和参数选择的重要性。通过实验验证了该算法的有效性,并以峰值信噪比（PSNR）为评价准则,利用多项式拟合方法选择了最优参数。引入边缘保持指数(EPI),与其他滤波算法比较,本算法在去除噪声的同时较好地保持了边缘。     

Optimal parameters identification and sensitivity study for abrasive waterjet milling model

In this paper we present the work related to the parameters identification for abrasive waterjet milling (AWJM) model that appears as an ill-posed inverse problem. The necessity of studying this problem comes from the industrial milling applications where the possibility to predict and model the final surface with high accuracy is one of the primary tasks in the absence of any knowledge of the model parameters that should be used. The adjoint approach based on corresponding Lagrangian gives the opportunity to find out the unknowns of the AWJM model and their optimal values that could be used to reproduce the required trench profile. Due to the complexity of the nonlinear problem and the large number of the model parameters, we use an automatic differentiation software tool. This approach also gives us the ability to distribute the research on more complex cases and consider different types of model errors and 3D time dependent model with variations of the jet feed speed. This approach gives us a good opportunity to identify the optimal model parameters and predict the surface profile both with self-generated data and measurements obtained from the real production. Considering different types of model errors allows us to receive the results acceptable in manufacturing and to expect the proper identification of unknowns.     

基于矩形NAM和偏微分方程的灰度图像压缩方法

借助矩形NAM图像表示方法和偏微分方程技术,提出一种新的灰度图像压缩方法.该方法在编码端把原始图像逆布局为若干矩形子块,并采用坐标压缩方法存储每个子块的位置、大小.在解码端,采用偏微分方程进行图像修复,有效消除解码图像中的方块效应.该方法的时间复杂度为 ,其中n为灰度图像像素数.实验表明:在保持图像质量的前提下,该方法具有更高的压缩比和更少的块数,具有较高实用价值.     

Mumford-Shah Regularizer with Contextual Feedback

We present a simple and robust feature preserving image regularization by letting local region measures modulate the diffusivity. The purpose of this modulation is to disambiguate low level cues in early vision. We interpret the Ambrosio-Tortorelli approximation of the Mumford-Shah model as a system with modulatory feedback and utilize this interpretation to integrate high level information into the regularization process. The method does not require any prior model or learning; the high level information is extracted from local regions and fed back to the regularization step. An important characteristic of the method is that both negative and positive feedback can be simultaneously used without creating oscillations. Experiments performed with both gray and color natural images demonstrate the potential of the method under difficult noise types, non-uniform contrast, existence of multi-scale patterns and textures.