On the convergence of stationary sequences in topology optimization

We consider structural topology optimization problems including unilateral constraints arising from non‐penetration conditions in contact mechanics. The resulting non‐convex non‐smooth problems are instances of mathematical programs with equilibrium constraints (MPEC), or bi‐level programs. Applying nested (implicit programming) algorithms to this class of problems is problematic owing to the singularity of the feasible set. We propose a perturbation strategy combining the relaxation of the equilibrium constraint with the restriction of the design domain to its regular part only. This strategy allows us to attack the problem numerically using standard non‐linear programming algorithms. We rigorously study the optimality conditions for the original singular problem as well as the convergence of stationary points and globally optimal solutions to approximating problems towards respective stationary points and globally optimal solutions to the original problem. A limited numerical benchmarking of the algorithm is performed. Copyright © 2005 John Wiley & Sons, Ltd.     

一种基于四阶偏微分方程的噪声消除方法

介绍了一种基于四阶偏微分方程(PDE)噪声消除方法。采用分片平面图像逼近被处理图像。在噪声消除同时保持良好边缘,避免了使用二阶偏微分方程处理图像常常出现的块效应。实验结果表明该方法是行之有效的。     

一种数字图像盲增强的新算法

给出一种数字图像盲增强的新算法. 其中源数字图像及其灰度级未知, 已知的仅仅是被噪声污染了的图像. 该算法首先估计密度函数, 然后估计图像的灰度级, 最后去噪声重建图像, 达到图像增强的目的. 仿真例子说明了该算法的有效性.     

On the H fixed-lag smoothing: how to exploit the information preview

The problem of the continuous-time H^∞ fixed-lag smoothing over the infinite horizon is studied. The first solution to the problem is derived in terms of one algebraic Riccati equation of the same dimension as in the filtering case and the mechanism by which the performance improvements with respect to the H^∞ filtering occur is clarified. It is shown that the H^∞ smoother exploits the information preview in an “H² manner”.     

深度图像的平滑

由于受到各种干扰，结构光方法获取的深度图像重建结果中包含大量的毛刺，本文将平面图像平滑的方法拓展到深度图像领域，通过分析噪声模型，我们利用中值滤波器和高斯滤波器对深度图像进行三维平滑。结合去噪电路，取得了满意的重建效果。     

求非光滑方程的半光滑牛顿方法

非光滑优化是数学规划中的一个非常活跃的研究方向 ,它起源于现实问题并在许多方面有着广泛的应用。它提供了一个研究规划中许多重要问题的统一框架。Pang和Qi[1 ]在研究互补问题、变分不等式问题和优化问题时 ,总结了八大类可以化为非光滑方程的问题。半光滑方法是求解非光滑问题的一类重要方法 ,它推广了求解光滑方程的牛顿方法 ,对于设计快速收敛的算法有着重要的意义。本文我们回顾总结求解非光滑方程的半光滑牛顿方法方面的进展 ,并给出一些建议     

B样条曲面在严格约束状态下的光顺拟合

提出一种新的B样条曲面造型方法:光顺地拟合空间型值点且同时严格地通过其中部分点.运用Lagrange乘子的条件极值法并引入光顺加权项，求出位置偏离和形状弯曲的最小二乘解，可以得到被称为B样条光顺准拟合的良好造型曲面.这一方法在包含门窗的交通工具外壳曲面设计、机械产品装配联接件制造中具有明显的实用价值.     

A fast multilevel thresholding method based on lowpass and highpass filtering

A new method of thresholding a gray-scale image into a desired number of classes is proposed in this paper. The proposed method first evaluates the number of peaks in the histogram, then finds a suitable lowpass or highpass filter such that the number of peaks in the filtered histogram is equal to the desired number of classes. Then, valleys in the filtered histogram are used as thresholds. The proposed method is computationally fast and corresponds to human intuition. In the experiments, we compare the performance of our proposed method with other thresholding methods and the method is shown effective and efficient in multilevel thresholding.     

Bernoulli—Gaussian序列的检测方法研究

ＢｅｒｎｏｕｌｉＧａｕｓｓｉａｎ序列的检测问题存在于具有跳变输入的Ｋａｌｍａｎ滤波及最优平滑等实际应用中。基于系统频域特性和极大似然原理，得到了一种最优似然比检测指标，并给出了基于该指标的一种次优检测方法。实例仿真验证了方法的有效性。     

标准正则化理论的一些推广和应用

在标准正则化理论中建议一类局部相互作用场和自适应正则项。局部相互作用场包括通常的误差项和一窗口函数。窗口的大小，取向和形状可以视具体的应用加以调整。自适应正则项用来处理不连续变化。这两项导致一对称的能量泛函。最简单的梯度下降算法通常在参数变化和有噪声时也很稳定，有效。