广义行（列）对称矩阵的QR分解及其算法

对广义行（列）对称矩阵的QR分解和性质进行了研究,给出了广义行（列）对称矩阵的QR分解的公式和快速算法,它们可有效减少广义行（列）对称矩阵的QR分解的计算量与存储量,并且不会丧失数值精度。同时讨论了系统参数估计,推广和丰富了两文（邹红星,王殿军,戴琼海,等.行(或列)对称矩阵的QR分解.中国科学：A辑,2002,32(9):842-849;蔺小林,蒋耀林.酉对称矩阵的QR分解及其算法.计算机学报,2005,28(5):817-822）的研究内容,拓宽了实际应用领域的范围, 并修正了后者的错误。     

酉对称矩阵的QR分解及其算法

该文讨论了酉对称矩阵QR分解中Q矩阵和R矩阵与母矩阵的Q矩阵和R矩阵之间的定量关系．从矩阵正交相抵的概念出发,给出了矩阵酉相抵的概念,证明了酉对称矩阵与母矩阵之间的酉相抵性,得到了酉相抵矩阵的Moore—Penrose逆等一些新的结论．同时,给出了酉对称矩阵的QR分解及其Moore—Penrose逆矩阵的算法．     

行对称矩阵广义逆的快速求解公式

对行对称矩阵的QR分解进行了研究,在此基础上给出了求行对称矩阵广义逆的快速求解公式,并给出了证明。将QR分解方法应用于该类行对称矩阵的广义逆的求解过程,既利用了QR分解保证足够的精度,又可大大降低求解一类具有该结构矩阵的广义逆的计算量和存储量。     

基于她分解与多项式的无线传感器网络密钥算法

提出了基于QR分解与二元多项式的密钥建立与分配方案。该方案以二元多项式的计算结果作为无线传感器网络的密钥。二元多项式的其中一个参数由对称矩阵进行QR分解生成,节点部署后交换Q矩阵的行信息再与R矩阵的列信息相乘生成多项式的参数。多项式的另一个参数由各自生成的随机数确定。分析结果表明：该方案可以提高存储效率、网络连通性、抗捕获性能,并能提供额外的通信链路验证。     

MIMO-OFDM系统中基于QR分解的新型迭代检测算法

结合QR分解的迭代检测算法与连续干扰消除思想提出了一种新型的QR迭代检测算法。该算法充分利用最后检测层分集增益最高、性能最优的特点,在每一次QR分解之后,仅保留最后检测层的判决,在接收信号中消除已判决信号的干扰,并将信道矩阵中已判决信号的列删除,降低信道矩阵列的维数后,进行下一次QR分解,直到所有层的信号都检测出来。分析表明,新型QR迭代检测算法复杂度大约为连续干扰消除算法的1/8,约为传统迭代检测算法的1/2。仿真试验表明,对称系统中新型QR迭代检测算法性能与传统迭代检测算法基本保持一致,都要优于连续干扰消除算法。     

双递推最小二乘二阶统计盲信道识别和均衡算法

对于单输入一多输出(SIMO)FIR信道,文中提出一种基于二阶统计的自适应盲识别和均衡算法.首先,基于输入数据矩阵的QR分解把盲信道识别问题转换为低秩矩阵近似解.然后,应用双递推最小二乘(Bi-LS)子空间跟踪方法来推导快速递归盲信道识别算法.新算法仅需要O(md~2)计算复杂度或者O(md)如果仅是均衡,其中m为接收数据矢量的维数(或信道矩阵的行秩),而d是信号子空间维数(或信道矩阵的列秩).为了克服后向迭代的缺陷,也提出一种逆QR子空间跟踪和信道均衡递推算法.逆QR递推算法十分适合于脉动阵并行实现.模拟结果证明了所提出的算法对于信道识别和均衡的有效性.     

基于QR 分解的彩色图像自嵌入全盲水印算法

针对彩色图像的版权保护问题,基于QR 矩阵分解提出了一种自嵌入全盲水印算 法。先将原始图像的G 通道分量进行非下采样剪切波变换,再对得到的低频分量分块QR 分解, 通过判断各子块R 矩阵中第一行元素向量的l1 范数与所有子块R 矩阵第一行元素l1 范数均值之 间的大小关系生成特征水印。然后对B 通道分量DWT 变换后的低频分量进行分块QR 分解, 并通过修改该子块QR 分解后R 矩阵中第一行最后一列元素来嵌入特征水印。特征水印的生成 和嵌入在两个通道内独立完成,水印检测无需原始载体图像,算法无需借助外加水印信息即可 完成对图像版权的鉴别。实验结果表明,该算法在经历添加噪声、JPEG 压缩、缩放、剪切和行 偏移等常见攻击时,具有很强的鲁棒性。     

用于EVS的改进小波变换图像融合算法

为增强小波变换图像融合算法的实时性,提高视觉增强系统(EVS)可见光图像与红外图像实时融合的效率,提出了一种基于矩阵QR分解和小波变换的图像融合算法.该算法对原始图像的像素矩阵进行QR分解,再利用正交矩阵的性质,根据小波变换图像融合算法对QR分解得到的上三角矩阵进行分解融合,利用QR分解得到的正交矩阵逆变换得到融合图像.实验结果表明,该算法能获得较好的实时性,同时保证较好的融合效果.     

一种利用对称三角分解求解整周模糊度的方法

整周模糊度的求解是利用载波相位进行测量时的关键问题.采用了对系数矩阵进行QR分解的方法,用以降低矩阵的维数.模糊度搜索时,针对Z变换可能会引入多余误差,采用了对称三角分解法对协方差矩阵进行去相关处理.实验与仿真结果验证了该算法的有效性.     

不同矩阵分解方法对海洋数据同化的影响*

在海洋数据同化领域,集合最优插值方法中,矩阵求逆过程所使用的奇异值分解(singular value decomposition,SVD)十分耗时。对集合最优插值中逆矩阵的求逆过程进行优化,分别使用LU分解、Choleskey分解、QR分解来替代SVD分解。首先,通过LU分解(Choleskey分解或QR分解)得到相应的三角矩阵(或正交矩阵);然后,利用分解后的矩阵来实现相关逆矩阵的计算。由于LU分解、Choleskey分解、QR分解的算法复杂度都远小于SVD分解,因此改进后的同化程序能得到大幅度的性能提升。数值结果表明,所采用的三种矩阵分解方法相比于SVD分解,都能将集合最优插值的计算效率提升至少两倍以上。值得一提的是,在四种矩阵分解中Choleskey分解使得整个同化程序的性能达到了最优。     

A quasi-Newton method with Cholesky factorization

A quasi-Newton method for unconstrained minimization is presented, which uses a Cholesky factorization of an approximation to the Hessian matrix. In each step a new row and column of this approximation matrix is determined and its Cholesky factorization is updated. This reduces storage requirements and simplifies the calculation of the search direction. Precautions are taken to hold the approximation matrix positive definite. It is shown that under usual conditions the method converges superlinearly or evenn-step quadratic.     

A new and fast implementation for null space based linear discriminant analysis

In this paper we present a new implementation for the null space based linear discriminant analysis. The main features of our implementation include: (i) the optimal transformation matrix is obtained easily by only orthogonal transformations without computing any eigendecomposition and singular value decomposition (SVD), consequently, our new implementation is eigendecomposition-free and SVD-free; (ii) its main computational complexity is from a economic QR factorization of the data matrix and a economic QR factorization of a n×n matrix with column pivoting, here n is the sample size, thus our new implementation is a fast one. The effectiveness of our new implementation is demonstrated by some real-world data sets.     

可压缩传感重构算法与近似QR分解

讨论了可压缩传感CS重构算法,并提出了一种新的改进算法效率、提高图像质量的方法,即：测量矩阵的近似QR分解。精确的重构算法（极小化L0范数）是一个NP完全问题,而这种算法的一个近似估计（极小化L1范数）能够对信号或图像高效率地重构。本文研究了L1算法的重构效果,通过改变测量矩阵的奇异值能够提高算法的重构效率。对测量矩阵的近似QR分解进行了研究,并给出了对测量矩阵的一些改进和相关的实验。     

A blind double color image watermarking algorithm based on QR decomposition

In this paper, a novel blind image watermarking scheme based on QR decomposition is proposed to embed color watermark image into color host image, which is significantly different from using the binary or gray image as watermark. When embedding watermark, the 24-bits color host image with size of 512?×?512 is divided into non-overlapping 4?×?4 pixel blocks and each pixel block is decomposed by QR. Then, according to the watermark information and the relation between the second row first column coefficient and the third row first column coefficient in the unitary matrix Q, the 24-bits color watermark image with size of 32?×?32 is embedded into the color host image. In addition, the new element compensatory method is used in the upper-triangle matrix R for reducing the visible distortion. When extracting watermark, only the watermarked image is needed. Compared with other SVD-based methods, the proposed method does not have the false-positive detection problem and has lower computational complexity, that is, the average running time of the proposed method only needs 1.481403 s. The experimental results show that the proposed method is robust against most common attacks including JPEG compression, JPEG 2000 compression, low-pass filtering, cropping, adding noise, blurring, rotation, scaling and sharpening et al. Compared with some related existing methods, the proposed algorithm has stronger robustness and better invisibility.     

排序QR分解MIMO检测器在FPGA中的实现

对于MIMO系统而言,其复杂度主要集中在检测上。在分析现有MIMO检测算法的基础上,给出了一种新的基于Givens旋转的排序QR分解检测器的实现方法。该方法通过将复数域的矩阵进行对称变换,转化到实数域进行QR分解,大大降低了运算量。依据上述方法,给出了硬件实现流程和模块结构图。软件仿真和硬件实现结果表明该检测方法在保证检测性能的基础上,大大降低了其硬件实现的复杂度,节省了FPGA中宝贵的乘法器资源和逻辑资源,保证了后续MIMO原理样机的研制。     

The unitary interactor matrix and its estimation using closed-loop data

This paper is concerned with the factorization and estimation of the unitary interactor matrix or the time-delay matrix of multivariable systems. The important properties of the unitary interactor matrix for minimum variance control are discussed. An algorithm for factorization of the unitary interactor matrix from the Markov parameters is introduced. A method for direct estimation of the interactor matrix from closed-loop data is proposed. The proposed algorithm is evaluated by application to a simulated example, pilot-scale experiment and actual industrial data.     

The design and implementation of the parallel out‐of‐core ScaLAPACK LU,QR, and Cholesky factorization routines

This paper describes the design and implementation of three core factorization routines—LU, QR, and Cholesky—included in the out‐of‐core extension of ScaLAPACK. These routines allow the factorization and solution of a dense system that is too large to fit entirely in physical memory. The full matrix is stored on disk and the factorization routines transfer sub‐matrice panels into memory. The ‘left‐looking’ column‐oriented variant of the factorization algorithm is implemented to reduce the disk I/O traffic. The routines are implemented using a portable I/O interface and utilize high‐performance ScaLAPACK factorization routines as in‐core computational kernels. We present the details of the implementation for the out‐of‐core ScaLAPACK factorization routines, as well as performance and scalability results on a Beowulf Linux cluster. Copyright © 2000 John Wiley & Sons, Ltd.