Regularization of Discrete Ill-Posed Problems

The paper concerns conditioning aspects of finite-dimensional problems arising when the Tikhonov regularization is applied to discrete ill-posed problems. A relation between the regularization parameter and the sensitivity of the regularized solution is investigated. The main conclusion is that the condition number can be decreased only to the square root of that for the nonregularized problem. The convergence of solutions of regularized discrete problems to the exact generalized solution is analyzed just in the case when the regularization corresponds to the minimal condition number. The convergence theorem is proved under the assumption of the suitable relation between the discretization level and the data error. As an example the method of truncated singular value decomposition with regularization is considered. This revised version was published online in July 2006 with corrections to the Cover Date.     

用局部奇异值分解与改进LDA相结合的方法进行人脸识别

简要叙述人脸图像的标准化过程，特征脸，LDA算法的原理及实现过程。用PCA获取最佳描述特征，然后用LDA获取最佳分类特征，并用实验证明了这种方案的可行性。     

MIMO—OFDM系统中的基于等对角QR分解的联合收发机的性能研究

研究了一种对信道矩阵进行等对角QR分解的联合编／解码算法，与传统对信道矩阵进行SVD分解算法不同之处在于，该算法将MIMO信道分解为多个相同的并行子信道，与VBLAST检测算法结合起来具有复杂度低，易于实现的优点。仿真结果表明采用该算法的SER性能优于除MLD以外算法的性能，并进一步从信道容量的角度证明了采用该算法，在高信噪比下所获得的信道容量与注水功率算法和等功率算法是相同的。     

关于SVD图像水印算法的分析和改进

分析现有的利用奇异值分解的一些图像水印算法，指出其存在着对原始载体图像和随机选取的图像的误检测率高的问题.通过分析奇异值分解的性质，指出了造成以上问题的原因并构造了一种新的算法.实验表明新算法能够比较好地区别含水印图像和未含水印的原始载体图像，对随机选取的图像的误检测率也大大降低，同时保证了比较高的鲁棒性，有实用价值.     

基于SVD的二次型距离相似索引层次算法

大容量多媒体数据库的基于内容相似性的检索本质上是高维特征空间中一定距离函数的 K近邻问题。对适合人类视觉的二次型距离函数 ,即使采用相似索引 ,当特征空间维数较高时检索仍不能保证实时性。为了解决此问题 ,提出基于 SVD(Singular Value Decomposition)的二次型距离相似索引层次算法 ,先以相似索引为基础在主导特征的子空间上进行代价低的近似检索 ,再对过滤结果在高维特征空间中进行线性的精确检索。实验证明 :该方法具有正确性、有效性和实时性     

Analysis of Henrici's Transformation for Singular Problems

Henrici's transformation is the underlying scheme that generates, by cycling, Steffensen's method for the approximation of the solution of a nonlinear equation in several variables. The aim of this paper is to analyze the asymptotic behavior of the obtained sequence (s _n ^* ) by applying Henrici's transformation when the initial sequence (s _n ) behaves sublinearly. We extend the work done in the regular case by Sadok [17] to vector sequences in the singular case. Under suitable conditions, we show that the slowest convergence rate of (s _n ^* ) is to be expected in a certain subspace N of R ^p . More precisely, if we write s _n ^* =s _n ^* ,N+s _n ^* ,N, the orthogonal decomposition into N and N , then the convergence is linear for (s _n ^* ,N) but ( _n ^* ,N) converges to the same limit faster than the initial one. In certain cases, we can have N=R ^p and the convergence is linear everywhere.     

基于小波变换和奇异值分解相结合的加密图像数字水印算法

以一种加密算法和多级小波变换,奇异值分解为基础,提出一种数字水印算法.将原始图像进行多级小波分解,然后对低频部分进行奇异值变换,将加密的水印信息嵌入其中.实验结果表明:该算法不仅具有较好的不可感性,而且对几何变换,如旋转、剪切、镜像,叠加噪声如椒盐、高斯噪声及高斯滤波等均具有很好的鲁棒性.     

Singular Value Decomposition Solution of the Schrödinger Equation in the Presence of Exchange Terms

A new numerical method of solving integro-differential equations appearing in the theory of atomic and nuclear scattering systems has been devised. It is termed Singular Value Decomposition Method (SVD). It consists in expanding the exchange kernel into a number of separable terms by means of the Singular Value Decomposition and then iterating over the remainder. In this paper, we extend our SVD method to the scattering of low energy electron-helium which has been the subject of interest, both theoretically and experimentally. We compare our results with the Moments Method which is widely used. The Moments Method consists of making an expansion of the solution into an especially favorable basis that takes care of the non-exchange part of the Hamiltonian.     

海洋环境探测分析雷达远距离回波信号的谱处理

利用海洋环境探测分析雷达提取海况参数的过程中，谱处理有着重要的意义。本文采用简洁的奇异值分解法进行定阶，并用一种新颖的噪声补偿措施来改进Ｂｕｒｇ算法，计算机仿真和实测数据处理均表明：该方法不仅能提取出傅里叶变换（ＦＴ）方法无从提取的信号，而且比Ｂｕｒｇ算法处理效果更好，更准确。     

矩阵方程AX=B,XC=D的定秩解

本文研究了一类矩阵方程组解的秩的范围.利用矩阵的奇异值分解以及Frobenius范数的特征,得到了解的极值秩以及解的通式,并就这些问题的特殊情况进行了讨论,得到了一些结果.