求解非负矩阵分解的子空间共轭梯度算法

交替最小二乘法由于其理论可靠性和实际有效性成为非负矩阵分解中备受欢迎的方法之一。文中基于交替最小二乘法将界约束优化中的积极集共轭梯度法运用到非负矩阵分解当中,算法在子问题的求解中,并利用子空间的思想来划分指标集,并利用文献CHENG Wangyou文中的共轭梯度法进行变量更新,在一定条件下证明了新算法的收敛性,实验结果表明算法是有效的。     

基于非负矩阵分解的多环芳烃成份识别

从重叠比较严重的混合物三维荧光光谱中恢复单一光谱信号,是光谱解析的难点。考虑到光谱内在的非负性,采用非负矩阵分解的投影梯度和交替最小二乘两种算法,并结合K均值初始化方法,来解析菲、芘、蒽3种芳烃混合物的三维荧光光谱数据,有效避免出现负数的分解结果,提取3种成份的三维荧光光谱,得到计算光谱与对应参考光谱的相似系数均大于0.970。计算结果表明,非负矩阵分解能够克服光谱重叠带来的干扰,有效提取光谱成份,从而实现对菲、芘、蒽的成份识别。其中,交替最小二乘的NMF算法更适合实时在线监测。     

基于约束非负矩阵分解的高光谱图像解混快速算法

约束非负矩阵分解是高光谱图像解混中常用的方法.该方法的求解通常采用投影梯度法,其收敛速度、求解精度和算法稳定性都有待提高.为此,本文针对较优的最小体积约束,提出一种基于约束非负矩阵分解的高光谱图像解混快速算法.首先优化原有的最小体积约束模型,然后设计了基于交替方向乘子法的非凸项约束非负矩阵分解算法,最后通过奇异值分解优化迭代步骤.模拟和实际数据实验结果验证了本文算法的有效性.     

基于四阶累积张量方法的欠定盲源信号分离

针对瞬时欠定盲源信号分离问题,提出一种四阶累积张量分解算法.首先构建观察信号四阶累积协方差,依据源信号具有相互独立且均值为零的性质,对累积协方差化简并扩展到张量域,得到四阶累积张量.采用分层交替最小二乘算法对四阶累积张量进行非负库克分解,求得非负库克模型的参数,同时获得非负混合矩阵并求其伪逆,最终估计出源信号.选用真实的语音信号和生物信号进行仿真实验,结果表明该方法提高了源信号和非负混合矩阵的估计性能.     

基于NMF和LS-SVM的肖像漫画生成算法研究

提出一种基于非负矩阵分解(NMF)和最小二乘支持向量机(LS-SVM)的肖像漫画生成算法.在训练阶段,利用非负矩阵分解来对夸张特征空间数据降维,运用最小二乘支持向量机(LS-SVM)统计学习夸张漫画与人脸之间的关系,建立形状夸张模型.在应用阶段,利用AAM算法提取人脸特征点,形状夸张模型计算出相应的漫画特征点数据,经过图像变形和风格化即可得到最终的肖像漫画.算法实验表明,该算法可以合理地夸张主要特征并避免过度变形.     

改进的非负矩阵分解语音增强算法

本文提出了一种改进的非负矩阵分解语音增强算法,该算法可分为训练和增强两部分。首先,为了降低训练复杂度,采用卷积非负矩阵分解只提取噪声字典。增强时,考虑语音信号稀疏性比噪声信号稀疏性强,通过稀疏非负矩阵分解重构出语音幅度谱,采用交替方向乘子法进行优化迭代,克服了经典乘性迭代易陷入局部最优、分母只能收敛到零极限等问题。最后,基于算法融合的思想,将重构的语音幅度谱与谱减法、最小均方误差幅度谱估计得到的幅度谱进行加权融合。仿真实验中,在10种不同噪声环境中,通过多种评价标准证明所提算法能取得较好的增强效果。      

非均匀噪声下频率及二维到达角的联合估计

提出一种适用于L型阵列的频率及二维到达角联合估计新算法.算法通过不同子阵的互协方差矩阵构建平行因子模型,应用三线性交替最小二乘算法求解,无需参数配对及多维搜索,可有效抑制非均匀噪声.均方根误差的仿真结果验证了该算法的有效性.     

MIMO系统中应用张量分解进行半盲信道估计的算法分析

针对多输入多输出系统半盲信道估计问题,提出一种基于张量分解的半盲联合信号检测和信道估计算法。其思想是利用张量分解的唯一性,对接收信号构造基于张量分解的平行因子模型,并利用正则交替最小二乘算法对信道和发送信号进行联合迭代估计。仿真结果表明:与传统基于导频信道估计方法相比,所提算法只需少量的导频序列即可获得较高的信道估计精度;与已有的交替最小二乘算法相比,所提算法消除了矩阵求伪逆时可能带来的病态问题,收敛速度较快。文章还详细的分析了正则系数和收敛条件等参数对正则交替最小二乘算法性能的影响。      

一种快速非负矩阵分解的人脸识别算法

用于人脸识别的非负矩阵分解算法,虽可提高图像识别率,但因其是通过迭代方法同时计算出基矩阵和系数矩阵,故当迭代次数较多时,计算过程耗时长。文中将二维线性判别分析方法与非负矩阵分解方法融合,提出了一种快速的双边二维非负矩阵分解算法。通过在AR、Ｙale人脸数据库上的实验结果显示,较二维双边非负矩阵分解算法,文中算法不仅使得训练时间大幅减少,而且识别率也有所提高。     

一种新的波达方向估计子空间算法研究

MUSIC算法是一种属于特征结构的子空间超分辨方法。该算法性能优良，但需要进行矩阵特征分解，运算量大。对波达方向估计问题进行了研究并提出了一种新的子空间算法。该算法利用总体最小二乘（TLS）方法取代特征分解得到噪声子空间,运算复杂度低于MUSIC算法，使其实时实现成为可能。总体最小二乘处理减轻了噪声的影响,该算法性能与MUSIC算法相当。理论分析和计算机仿真结果表明此方法是有效的。     

An Effective Multigrid Preconditioned CG Algorithm for Millimeter Wave Scattering by an Infinite Plane Metallic Grating

An effective multigrid based preconditioned conjugate gradient method is developed to solve electromagnetic large matrix problem for millimeter wave scattering application. By using multigrid technique we restrict the large matrix equation to a relative smaller matrix and which can be solved rapidly. The solution is prolonged as the initial guess for the conjugate gradient (CG) method. Numerical results show that our developed method can reach five times improvement of computational complexity.     

Performance analysis of structured gradient algorithm [antennaarray processing]

The structured gradient algorithm uses a structured estimate of the array correlation matrix to estimate the gradient required for the constrained least mean square algorithm. This structure reflects the structure of the exact array correlation matrix for an equispaced linear array and is obtained by spatial averaging of the elements of the noisy correlation matrix. In its standard form the LMS algorithm does not exploit the structure of the array correlation matrix. The gradient is estimated by multiplying the array output with the receiver outputs. An analysis of the two algorithms is presented to show that the covariance of the gradient estimated by the structured method is less sensitive to the look direction signal than that estimated by the standard method. The effect of the number of elements on the signal sensitivity of the two algorithms is studied     

Analysis of Millimeter Wave Scattering by an Electrically Large Metallic Grating Using Wavelet-Based Algebraic Multigrid Preconditioned CG Method

An effective wavelet based multigrid preconditioned conjugate gradient method is developed to solve electromagnetic large matrix problem for millimeter wave scattering application. By using wavelet transformation we restrict the large matrix equation to a relative smaller matrix and which can be solved rapidly. The solution is prolonged as the new improvement for the conjugate gradient (CG) method. Numerical results show that our developed wavelet based multigrid preconditioned CG method can reach large improvement of computational complexity. Due to the automaticity of wavelet transformation, this method is potential to be a block box solver without physical background.     

一种改进的基于区域梯度——能量的图像融合方法

针对区域梯度法、区域能量法重构图像峰值信噪比较低、均方根误差较高的现象,提出了一种改进的基于区域梯度-能量的压缩感知图像融合方法。该方法首先构造正交小波变换矩阵,并使用小波变换使图像稀疏化,然后采用哈达玛矩阵作为测量矩阵对稀疏信号进行测量得到测量值,分别计算测量值对应的梯度值及能量值,依据绝对值取大法及加权平均法对测量值进行融合,最后对融合后的测量值进行图像重构。实验结果表明,该方法比单独使用区域梯度法或区域能量法具有较好的图像融合效果。     

一种基于四阶循环累积量的盲源分离方法

盲源分离是指在没有源信号任何先验知识的情况下,只根据多个接收机的观测信号实现对源信号的恢复。本文基于四阶循环累积量提出了一种简单易行的循环平稳信号的盲源分离方法。针对两个信号混合的情况,该方法首先对观测矩阵进行循环白化,使得观测矩阵的循环自相关阵为单位阵,这样分离矩阵变为酉阵,可用单个参数来表示。之后运用循环统计量的性质找到一个评判函数,求得该参数的最佳值从而确定分离矩阵。本文对BPSK信号和AM信号混合的情况分别进行了仿真实验,通过信号分离的直观图、参数选择以及串音误差的分析表明该方法的有效性,并将其与自然梯度算法,循环自然梯度算法做了比较,表明本算法的优势,尤其是在AM信号的分离中更是如此。文章最后讨论了算法的运行时间。      

Analysis of constrained LMS algorithm with application to adaptive beamforming using perturbation sequences

Adaptive antenna array processing employing a constrained least mean square (LMS) algorithm requires an unbiased estimate of the gradient of the output power with respect to the array weights. There are a number of schemes for obtaining an unbiased estimate of this gradient. Though in each case the estimated gradient is unbiased, the covariance of the estimated gradient with each method is different and thus the transient and the steady state behavior of the constrained algorithm is different in each case. The transient and the steady state behavior of the weight covariancc matrix is analyzed, exact expressions for the misadjustment are derived, and a comparison of the performance of the algorithm is presented when the required gradient is estimated by different schemes. The schemes considered include gradient estimation when all the array signals are accessible as well as gradient estimation using perturbation sequences for eases when the array signals are inaccessible. The necessary and the sufficient condition for the diagonlization of the weight covarience matrix is also derived.     

基于互信息梯度优化计算的信息判别特征提取

该文将互信息梯度优化引入特征提取矩阵求解,提出一种信息判别分析的特征提取方法。首先,分析了现有线性判别方法的特点和局限,建立了类条件分布参数模型下互信息最大化的信息判别模型。其次,证明了互信息判别的线性变换不变性和贝叶斯一致优化,构造了一个互信息梯度优化计算的特征提取算法。最后通过实际数据上试验验证了该方法的有效性。     

Banded matrix iterative approach to Monte-Carlo simulations of scattering of waves by large-scale random rough surface problems: TM case

A banded matrix iterative approach is applied to study the scattering of a TM incident wave from a perfectly conducting one-dimensional random rough surface. It is accurate and is much faster than the full matrix inversion approach or the conjugate gradient method. Applications of this method to large-scale rough surface problems are illustrated.<>     

Regularization of the moment matrix solution by a nonquadraticconjugate gradient method

Inspired by Tikhonov regularization, a nonlinear conjugate gradient method is proposed with the purpose of simultaneously regularizing and solving the moment matrix equation. The procedure is based on a nonquadratic conjugate gradient algorithm with exact line search, restart, and rescale. Applied to the problem of TM scattering by perfectly conducting rectangular cylinders, the method is shown to exhibit a fast convergence rate     

Covariance matrix based fast smoothed sparse DOA estimation with partly calibrated array

To solve the problem of direction-of-arrival (DOA) estimation for partly calibrated array, a new gain-phase error matrix estimation scheme and a smoothed sparse signal reconstruction method tailored for the complex-valued covariance matrix are proposed. In the proposed method, DOA estimation is achieved by employing the structure of the covariance matrix for the error matrix estimation and the complex-valued gradient matrix based fast non-convexity data reconstruction. The proposed method has much faster computational speed than other sparse DOA estimation methods with partly calibrated array. In addition, simulation results show that it performs well and is independent of the errors.