二维正交小波滤波器的逼近

提出了一种二维正交小波滤波器逼近的方法,采用分步优化的方法来构造小波滤波器,最后通过实验给出低通的小波滤波器.     

带NCP函数的信赖域滤子方法

滤子方法最初是由Fletcher和Leyffer在2002年提出的.这种方法的原理是:在一个试探步,如果相应的目标函数值或约束违反度函数值下降,那么该试探步就会被接受.利用Fischer-Burmeister NCP函数来修正滤子中的约束违反度函数,同时证明了这个新的滤子方法具有全局收敛性.     

一种新的结合NCP函数的SQP滤子算法

对于SQP滤子算法,本文提出了一种新方法来构造滤子,目的是为了使滤子的接受条件更宽松,降低进行可行性恢复的机率.另外,本文通过一些数值例子对这种新算法进行了检验,事实证明这种算法是有效的.最后还证明这种算法具有超线性收敛性.     

An SQP-filter method for inequality constrained optimization and its global convergence

In this paper, we combine the filter technique with a modified sequential quadratic programming (SQP) method. The optimization solution is obtained by reducing step length, which is obtained by an exact linear search. Furthermore, this method can start with an infeasible initial point. The method uses a filter to promote global convergence.     

新的滤子方法

本文定义了一种新的滤子方法,并提出了求解光滑不等式约束最优化问题的滤子QP-free非可行域方法.通过乘子和分片线性非线性互补函数,构造一个等价于原约束问题一阶KKT条件的非光滑方程组.在此基础上,通过牛顿-拟牛顿迭代得到满足KKT最优条件的解,在迭代中采用了滤子线搜索方法,证明了该算法是可实现,并具有全局收敛性.另外,在较弱条件下可以证明该方法具有超线性收敛性.     

A modified SQP-filter method for nonlinear complementarity problem

The nonlinear complementarity problem can be reformulated as a nonlinear programming. For solving nonlinear programming, sequential quadratic programming (SQP) type method is very effective. Moreover, filter method, for its good numerical results, are extensively studied to handle nonlinear programming problems recently. In this paper, a modified quadratic subproblem is proposed. Based on it, we employ filter technique to tackle nonlinear complementarity problem. This method has no demand on initial point. The restoration phase, which is always used in traditional filter method, is not needed. Global convergence results of the proposed algorithm are established under suitable conditions. Some numerical results are reported in this paper.     

结合滤子技术的牛顿折线法及其实现

成功将多维滤子技术应用到牛顿折线法,提出了多维滤子牛顿折线法.新算法增加了牛顿点以及信赖域的试探点被接收作为下一步迭代点的几率.在一定的假设条件下证明了算法的全局收敛性.数值试验表明,滤子牛顿折线法适合于求解等势线呈峡谷状的函数.     

An Improved Method for Designing Quadrature Mirror Filter Banks via Unconstrained Optimization

This paper proposes an algorithm to design a two-channel linear phase quadrature mirror filter (QMF) bank. The design problem is presented systematically as an unconstrained optimization that minimizes the weighted sum of error of transfer function of the filter bank at quadrature frequency, stopband energy and the passband error of a prototype filter (PF). A new method is developed for the design of a low pass prototype filter for QMF banks. For solving given optimization problem, Quasi-Newton optimization technique is used. Numerical examples and comparisons with several existing methods are included to show the performances and effectiveness of this method. An application of the proposed method is considered in the area of subband coding of the images.     

基于模糊中值滤波的椒盐噪声去除方法

研究基于模糊中值滤波的椒盐噪声去除方法。通过比较图像各像素点的灰度值,定义基于图像梯度信息的各点被判别为噪声点的模糊隶属函数。利用此模糊隶属函数对中值滤波方法进行加权,得到了一种加权中值滤波器,可实现边缘处椒盐噪声的有效滤除。讨论这种模糊加权方法与其它先进滤波方法的结合途径,指出了其推广应用价值。最后利用数值实验验证本文方法的有效性,结果表明,相比于自适应中值滤波方法,本文方法得到的滤波图像在峰值信噪比及结构相似度方面均有明显提高。     

Convergence of a Three-Dimensional Dwindling Filter Algorithm Without Feasibility Restoration Phase

In this article, we propose a three-dimensional dwindling filter algorithm for general nonlinear programming. The envelope of the three-dimensional dwindling filter becomes thinner and thinner as the step size approaches zero so that the new filter has more flexibility for the acceptance of the trial step size. Moreover, we show that the feasibility restoration phase, which is always used in traditional filter method, is not needed. The modified limited memory Broyden-Fletcher-Goldfarb-Shanno method is employed in the algorithm, and the update matrices are positive definite when the Lagrangian function is a general convex function. Under mild conditions, the global convergence of the new algorithm is analyzed. The primary numerical experiments are reported to show effectiveness of the proposed algorithm.     

小波分式滤波器

1．引言用小波处理实际问题时，对称性具有重要的意义．如果小波不具有对称性，则在信号重构时可能导致失真．我们知道，用多项式滤波器构造的正交小波不具有对称性，这是一个重要的缺欠．本文讨论了分式滤波器，它作为多项式滤波器的最自然的推广和进展，且包含了B样条小波滤波器，可随意构造出对称性小波函数，对实际应用提供了有意义的构造性方法．在小波计算中，为了回避hllrl＊r逆变换，人们通常喜欢用Mdl时算法山，即对尺度函数方程为造迭代格式为了得到迭代收敛（n。、v）条件，通常把滤波器其中以及时，迭代格式（2）逐点收敛于尺…     

结合有效集和多维滤子技术的拟Newton信赖域算法(英文)

针对界约束优化问题,提出一个修正的多维滤子信赖域算法.将滤子技术引入到拟Newton信赖域方法,在每步迭代,Cauchy点用于预测有效集,此时试探步借助于求解一个较小规模的信赖域子问题获得.在一定条件下,本文所提出的修正算法对于凸约束优化问题全局收敛.数值试验验证了新算法的实际运行结果.     

新的滤子方法(英)

本文定义了一种新的滤子方法,并提出了求解光滑不等式约束最优化问题的滤子QP-free非可行域方法. 通过乘子和分片线性非线性互补函数,构造一个等价于原约束问题一阶KKT条件的非光滑方程组.在此基础上, 通过牛顿-拟牛顿迭代得到满足KKT最优条件的解,在迭代中采用了滤子线搜索方法,证明了该算法是可实现,并具有全局收敛性. 另外,在较弱条件下可以证明该方法具有超线性收敛性.     

3-分片线性NCP函数的滤子QP-free算法

本文定义一个3-分片线性的NCP函数,并对非线性约束优化问题,提出了带有这分片NCP函数的QP-free非可行域算法.根据优化问题的一阶KKT条件,利用乘子和NCP函数,得到非光滑方程,本文给出一个非光滑方程的迭代算法.这算法包含原始-对偶变量,在局部意义下,可看成关于一阶KKT最优条件的的扰动拟牛顿迭代算法.在线性搜索时,这算法采用滤子方法.本文给出的算法是可实现的并具有全局收敛性,且在适当假设下具有超线性收敛性.     

正交共轭滤波器的构造

It is very importent for generating an orthonormal multiwavelet system to construct a conjugate quadrature filter(CQF). In this paper, a general method of deriving a length-L 1 conjugate quadrature filter from a length-L conjugate quadrature filter and vice versa is obtained. As a special case, we study generally the construction of any length-L 1 compactly supported symmetric-antisymmetric orthonormal multiwavelet system with multiplicity 2 from a length-L multiwavelet system and vice versa. Examples of conjugate quadrature filter are given.     

分片线性NCP函数滤子QP-free算法

本文定义了分片线性NCP函数,并对非线性约束优化问题,提出了带有这分片NCP函数的QP-free非可行域算法.利用优化问题的一阶KKT条件,乘子和NCP函数,得到对应的非光滑方程组.本文给出解这非光滑方程组算法,它包含原始-对偶变量,在局部意义下,可看成关扰动牛顿-拟牛顿迭代算法.在线性搜索时,这算法采用滤子方法.本文给出的算法是可实现的并具有全局收敛性,在适当假设下算法具有超线性收敛性.     

A kind of nonmonotone filter method for nonlinear complementarity problem

The nonlinear complementarity problem can be reformulated as a nonlinear programming. For solving nonlinear programming, sequential quadratic programming (SQP) type method is very effective. But the QP subproblem may be inconsistent. In this paper, we propose a kind nonmonotone filter method in which the QP subproblem is consistent. By means of nonmonotone filter, this method has no demand on the penalty parameter which is difficult to obtain. Moreover, the restoration phase is not needed any more. Under reasonable conditions, we obtain the global convergence of the algorithm. Some numerical results are presented.     

Non‐separable multivariate filter banks from univariate wavelets

The main purpose of this paper is the design of multivariate filter banks starting from univariate wavelet filters. The matrix completion is solved by utilizing some special Toeplitz matrices. A generalized method of rational polynomial univariate filter with preset zero points set is constructed.     

On the fractional-order extended Kalman filter and its application to chaotic cryptography in noisy environment

In this paper via a novel method of discretized continuous-time Kalman filter, the problem of synchronization and cryptography in fractional-order systems has been investigated in presence of noisy environment for process and output signals. The fractional-order Kalman filter equation, applicable for linear systems, and its extension called the extended Kalman filter, which can be used for nonlinear systems, are derived. The result is utilized for chaos synchronization with the aim of cryptography while the transmitter system is fractional-order, and both the transmitter and transmission channel are noisy. The fractional-order stochastic chaotic Chen system is then presented to apply the proposed method for chaotic signal cryptography. The results show the effectiveness of the proposed method.     

A modified SLP algorithm and its global convergence

This paper concerns a filter technique and its application to the trust region method for nonlinear programming (NLP) problems. We used our filter trust region algorithm to solve NLP problems with equality and inequality constraints, instead of solving NLP problems with just inequality constraints, as was introduced by Fletcher et al. [R. Fletcher, S. Leyffer, Ph.L. Toint, On the global converge of an SLP-filter algorithm, Report NA/183, Department of Mathematics, Dundee University, Dundee, Scotland, 1999]. We incorporate this filter technique into the traditional trust region method such that the new algorithm possesses nonmonotonicity. Unlike the tradition trust region method, our algorithm performs a nonmonotone filter technique to find a new iteration point if a trial step is not accepted. Under mild conditions, we prove that the algorithm is globally convergent.