红外焦距仪系统中平滑去噪方法的研究

红外焦距仪系统中使用线阵CCD采集信号时，由于CCD本身的散粒噪声以及外界环境(如外界杂散光，信号光的光子起伏，电、磁干扰等)的影响，采集到的信号往往有一定程度的失真和变形，存在许多“毛刺”，不利于数据的计算和分析。本文采用3次B样条小波对原始信号进行分解，对分解后的数据进行平滑处理，最后重构得到平滑信号。该方法解决了线阵CCD采集信号的不平滑问题。     

函数mid(·)的一个光滑化函数及其性质

介绍了函数mid(·)可以把混合互补问题转化为一个等价的非光滑的方程组 ,由于其非光滑性 ,难以直接用光滑Newton法求解 ,光滑化就显得尤为重要 .文中采用熵摄动来光滑化函数mid(·) ,讨论了得到的光滑化函数的一些性质 .     

On the problems of smoothing and near-interpolation

In the first part of this paper we apply a saddle point theorem from convex analysis to show that various constrained minimization problems are equivalent to the problem of smoothing by spline functions. In particular, we show that near-interpolants are smoothing splines with weights that arise as Lagrange multipliers corresponding to the constraints in the problem of near-interpolation. In the second part of this paper we apply certain fixed point iterations to compute these weights. A similar iteration is applied to the computation of the smoothing parameter in the problem of smoothing.

     

平面凸轮廓线实测数据的光顺及拟合

本文分析了凸轮廓线二阶导数连续的必要性,提出了以凸轮廓线一阶差商、二阶差商、法线倾角和曲率的差商为判据,修正凸轮廓线型值点,并保证其满足光顺条件的方法。文中还给出了可用于凸轮廓线拟合的三次样条和圆弧样条的求解方法。     

Semi-classical smoothing in a non-monotonic field

It is pointed out that the semi-classical method of Jennings, Bhaduri and Brack for smoothing the total energy of a system of non-interacting fermions in a potential wellV(r) breaks down in the fourth-order term if this potential is non-monotonic. This means that the method as it stands can only be used by neglecting the Coulomb force on protons. We propose a modified treatment for the fourth-order term which appears to be entirely satisfactory.     

Nonlinear rescaling vs. smoothing technique in convex optimization

We introduce an alternative to the smoothing technique approach for constrained optimization. As it turns out for any given smoothing function there exists a modification with particular properties. We use the modification for Nonlinear Rescaling (NR) the constraints of a given constrained optimization problem into an equivalent set of constraints.?The constraints transformation is scaled by a vector of positive parameters. The Lagrangian for the equivalent problems is to the correspondent Smoothing Penalty functions as Augmented Lagrangian to the Classical Penalty function or MBFs to the Barrier Functions. Moreover the Lagrangians for the equivalent problems combine the best properties of Quadratic and Nonquadratic Augmented Lagrangians and at the same time are free from their main drawbacks.?Sequential unconstrained minimization of the Lagrangian for the equivalent problem in primal space followed by both Lagrange multipliers and scaling parameters update leads to a new class of NR multipliers methods, which are equivalent to the Interior Quadratic Prox methods for the dual problem.?We proved convergence and estimate the rate of convergence of the NR multipliers method under very mild assumptions on the input data. We also estimate the rate of convergence under various assumptions on the input data.?In particular, under the standard second order optimality conditions the NR method converges with Q-linear rate without unbounded increase of the scaling parameters, which correspond to the active constraints.?We also established global quadratic convergence of the NR methods for Linear Programming with unique dual solution.?We provide numerical results, which strongly support the theory. Received: September 2000 / Accepted: October 2001?Published online April 12, 2002     

基于改进蚁群算法的无人机动态航路规划

研究无人机航路规划,针对基本蚁群算法易于陷入局部最优、规划航路耗时长的问题,对基本蚁群算法进行了改进;引入航路点的动态自适应选择策略和信息素挥发因子动态自适应调整准则,有效克服了基本蚁群算法的不足,并对规划出的航路进行了平滑处理,使其更加满足无人机实际飞行需求。通过仿真分别规划出无人机在静态威胁和动态威胁中的航迹,仿真结果表明,与基本蚁群算法和遗传算法相比,改进的蚁群算法在两种飞行环境中均能规划出较优的航路。     

二元域上线性半群到任意域上线性半群的同态

群同态是群论研究的主要问题,F2上的半群同态也一直是群论研究者关注的热点问题.为探讨二阶线性半群间的同态问题,本文在引进标准型、延断型、平凡型概念的基础上,通过矩阵计算与群的定义关系,描述了F2上的线性半群Mn(F2)到任意域K上的线性半群Mm(K)的同态形式(n≥m2).给出了nm,乘法半群同态(不必保幺元)为In,s,r或为φ1的延断(其中:若X为GL2(F2)的2阶元,φ1(X)=-1;若X=I2或X为3阶元,φ1(X)=1);当n=m时,乘法半群同态(不必保幺元)除In,s,r外,为标准型或为线性非平凡解同态的延断.这些结果结合文献中已有的关于一般线性群及二阶线性半群的结果,完全描述了二元域上的线性半群到任意域上的线性半群的同态的形式.     

非线性互补问题的一个数值解法

提出了一个新的NCP光滑逼近函数,利用此光滑逼近函数把非线性互补问题转化为一个等价的方程组,在此基础上提出一个求解方程组的非单调光滑牛顿法,在适当的条件下证明了其全局和局部收敛性。数值试验说明了算法的有效性。     

混合噪声的图像复原算法

提出了一种基于中值滤波和局部线性核平滑的图像去噪算法.该算法采用在空间域中的自适应滤波思想,运用改进的混合滤波器去除图像中的混合噪声.该算法的特点是复原后的图像能较好地保留边缘,同时对图像退化的先验知识要求不严格,并且有明确的数学公式,更适合实际运用.实验表明,作者提出的方法对含有混合噪声的图像复原具有较好的效果.