Application of Robust Incomplete Cholesky Factorizations Preconditioned CG Algorithms for FEM Analysis of Millimeter Wave Filters

The Incomplete Cholesky factorizations preconditioning scheme is applied to the conjugate gradient (CG) method for solving a large system of linear equations resulting from finite element method (FEM) analysis of millimeter wave filters. As is well known, the convergence of CG method deteriorates with increasing EM wave number and in millimeter wave band the eigen-values of A are more and more scattered between both the right and the left half-plane. The efficient implementation of this preconditioned CG (PCG) algorithm is described in details for Complex coefficient matrix. With incomplete factorization preconditioning scheme in the conjugate gradient algorithm, this PCG approach can reach convergence in 20 times CPU time shorter than CG for several typical millimeter wave structures.     

Application of the SSOR preconditioned CG algorithm to the vectorFEM for 3D full-wave analysis of electromagnetic-field boundary-valueproblems

The symmetric successive overrelaxation (SSOR) preconditioning scheme is applied to the conjugate-gradient (CG) method for solving a large system of linear equations resulting from the use of edge-based finite-element method (FEM). For this scheme, there is no additional computing time required to construct the preconditioning matrix and it contains more global information of the coefficient matrix when compared with those of the banded-matrix preconditioning scheme. The efficient implementation of this preconditioned CG (PCG) algorithm is described in details for complex coefficient matrix. With SSOR as the preconditioner and its efficient implementation in the CG algorithm, this PCG approach can reach convergence in five times CPU time shorter than CG for several typical structures. By comparison with other preconditioned techniques, these results demonstrate that SSOR preconditioning strategy is especially effective for CG iterative method when an edge FEM is applied to solve large-scale time-harmonic electromagnetic-field problems     

湍流退化图像相位恢复算法研究

为克服气动光学效应对目标图像的影响．把相位恢复算法与气动光学效应机理研究结合起来,用于湍流退化图像的恢复。该算法是通过目标图像的傅里叶变换幅值来恢复目标图像,或等价地,恢复傅里叶变换相位。讨论了两类相位复原算法——迭代傅里叶变换（研）和解相关算法。对现有的解相关算法作了改进。采用共轭梯度法解高斯一牛顿方程,可有效提高算法的收敛速度。研算法不能保证迭代过程总能收敛到正确解,有时会出现停滞现象。将研和解相关算法组合起来,可以克服IFT算法的停滞现象,提高正确收敛率。给出了在信噪比为20dB情况下的湍流退化仿真图像恢复的实例,目标图像能较清晰地恢复出来。实验结果表明该算法具有较好的稳定性和抗噪声能力。     

Inverse scattering of two-dimensional dielectric objects buried ina lossy earth using the distorted Born iterative method

An efficient inverse-scattering algorithm is developed to reconstruct both the permittivity and conductivity profiles of two-dimensional (2D) dielectric objects buried in a lossy earth using the distorted Born iterative method (DBIM). In this algorithm, the measurement data are collected on (or over) the air-earth interface for multiple transmitter and receiver locations at single frequency. The nonlinearity due to the multiple scattering of pixels to pixels, and pixels to the air-earth interface has been taken into account in the iterative minimization scheme. At each iteration, a conjugate gradient (CG) method is chosen to solve the linearized problem, which takes the calling number of the forward solver to a minimum. To reduce the CPU time, the forward solver for buried dielectric objects is implemented by the CG method and fast Fourier transform (FFT). Numerous numerical examples are given to show the convergence, stability, and error tolerance of the algorithm     

基于平行因子分解的大规模MIMO盲信道估计

针对单小区大规模多输入多输出（Multiple-Input Multiple-Output,MIMO）系统上行链路,提出了一种基于平行因子（Parallel Factor,PARAFAC）模型的信道估计方法。在基站端,将接收信号构造成PARAFAC模型,利用大规模MIMO系统中信道的渐近正交的性质,提出了一种基于约束二线性迭代最小二乘算法(Constrained Blinear Alternating Least Squares,CBALS),从而实现了盲信道估计。理论分析及仿真结果表明,所提方法与传统最小二乘方法相比,不仅提高了频带利用率而且具有更高的估计精度;与已有的二线性交替最小二乘方法(BALS)相比,所提算法有更快的收敛速度。     

Nonlinear adaptive bilinear filters for active noise control systems

The reference and error channels of active noise control (ANC) systems may be saturated in real-world applications if the noise level exceeds the dynamic range of the electronic devices. This nonlinear saturation degrades the performance of ANC systems that use linear adaptive filters with the filtered-X least-mean-square (FXLMS) algorithm. This paper derives a bilinear FXLMS algorithm for nonlinear adaptive filters to solve the problems of signal saturation and other nonlinear distortions that occur in ANC systems used for practical applications. The performance of this bilinear adaptive filter is evaluated in terms of convergence speed, residual noise in steady state, and the computational complexity for different filter lengths. Computer simulations verify that the nonlinear adaptive filter with the associated bilinear FXLMS algorithm is more effective in reducing saturation effects in ANC systems than a linear filter and a nonlinear Volterra filter with the FXLMS algorithm.     

基于微分搜索的高光谱图像非线性解混算法

针对线性混合模型在实际高光谱图像解混过程中的局限性,提出一种新的基于微分搜索的非线性高光谱图像解混算法.在广义双线性模型的基础上采用重构误差作为解混的目标函数,将非线性解混问题转化为最优化问题.将目标函数中的待求参数映射为微分搜索过程中的位置变量,利用微分搜索算法对目标函数进行优化求解.在求解过程中,通过执行搜索范围控制等机制满足高光谱图像解混的约束要求,进而求得丰度系数和非线性参数,实现非线性高光谱图像解混.仿真数据和真实遥感数据实验结果表明,所提出的非线性解混算法可以有效克服线性模型下解混算法的局限性,避免了由于使用梯度类优化方法而易陷入局部收敛的问题,较之其它高光谱图像解混算法具有更好的解混精度.     

Analysis of conjugate gradient algorithms for adaptive filtering

The paper presents and analyzes two approaches to the implementation of the conjugate gradient (CG) algorithm for filtering where several modifications to the original CG method are proposed. The convergence rates and misadjustments for the two approaches are compared. An analysis in the z-domain is used in order to find the asymptotic performance, and stability bounds are established. The behavior of the algorithms in finite word-length computation are described, and dynamic range considerations are discussed. It is shown that in finite word-length computation and close to steady state, the algorithms' behaviors are similar to the steepest descent algorithm, where the stalling phenomenon is observed. Using 16-bit fixed-point number representation, our simulations show that the algorithms are numerically stable     

Eigenvalues of the moment-method matrix and their effect on theconvergence of the conjugate gradient algorithm [EM scattering]

A theory that relates eigenvalues of a continuous operator to those of the moment-method matrix operator is discussed and confirmed by examples. This theory suggests reasons for ill conditioning when certain types of basis and testing functions are used. In addition, the effect of eigenvalue location on the convergence of the conjugate gradient (CG) method is studied. The convergence rate of the CG method is dependent on the eigenvalues of the iteration matrix as well as on the number of eigenvectors of the iteration matrix needed to represent the right side of the equation. These findings explain the previously reported convergence behavior of the CG method when applied to electromagnetic-scattering problems     

双线性反馈神经网络的复值盲均衡算法研究

将基于双线性反馈神经网络的盲均衡算法运用到了复数系统中,推导了复数系统中网络的权值迭代公式,运用QAM信号对算法进行仿真表明,算法对于QAM信号的均衡有着较快的收敛速度和较低的误码率。     

基于MG-CG算法的图像超分辨率重建

提出一种基于多重网格(MG)和共扼梯度(CG)算法相结合的图像超分辨率重建快速算法.首先采用Tikhonov正则化方法给出图像超分辨率重建模型;然后在系统介绍MG和CG算法的基础上,针对超分辨率重建中常见对称正定稀疏线性方程的求解,提出多重网格-共扼梯度(MG-CG)算法;详细讨论了MG-CG算法的光滑、限制、插值操作以及计算复杂度.实验结果表明该算法与MG、CG和Richardson迭代算法相比,具有更快的收敛速度.     

A VLSI-oriented algorithm and its implementation for AVS chroma interpolation

AVS (audio video coding standard) is the latest multimedia coding standard of China. Similar to H.264/AVC, AVS adopted the technology of fractional-pel-accurate motion compensation, which enhanced the compression efficiency. To obtain fractional pels, 4-tap FIR filters and bilinear filters are used for luma and chroma interpolation respectively. Unlike the VLSI-optimized FIR filters which could be implemented by adders and shifters, the bilinear filter for chroma is not so convenient for direct VLSI implementation due to its multiplications. In this paper, we propose a VLSI-oriented algorithm named SHAM (x–y-separated halved-approaching method) to accomplish the bilinear filtering. The proposed SHAM algorithm adopts a halved-approaching method which is an addition-and-shift-only method and with simpler data path. VLSI structures are also provide to implement the SHAM algorithm in this paper. Experiments based on UMC $0.18\mathrm{\mu }\mathrm{m}$ process show that the SHAM algorithm could be implemented with about 48% less silicon area or at doubled frequency compared with the direct implementation of the bilinear filter.     

A robust past algorithm for subspace tracking in impulsive noise

The PAST algorithm is an effective and low complexity method for adaptive subspace tracking. However, due to the use of the recursive least squares (RLS) algorithm in estimating the conventional correlation matrix, like other RLS algorithms, it is very sensitive to impulsive noise and the performance can be degraded substantially. To overcome this problem, a new robust correlation matrix estimate, based on robust statistics concept, is proposed in this paper. It is derived from the maximum-likelihood (ML) estimate of a multivariate Gaussian process in contaminated Gaussian noise (CG) similar to the M-estimates in robust statistics. This new estimator is incorporated into the PAST algorithm for robust subspace tracking in impulsive noise. Furthermore, a new restoring mechanism is proposed to combat the hostile effect of long burst of impulses, which sporadically occur in communications systems. The convergence of this new algorithm is analyzed by extending a previous ordinary differential equation (ODE)-based method for PAST. Both theoretical and simulation results show that the proposed algorithm offers improved robustness against impulsive noise over the PAST algorithm. The performance of the new algorithm in nominal Gaussian noise is very close to that of the PAST algorithm.     

FPGA实现的视频图像缩放显示

对几种常用的图像缩放算法进行了比较,在权衡了算法复杂度、缩放效果和FPGA逻辑资源等3大因素后,选择了双线性插值算法来实现图像缩放。重点介绍了双线性插值算法和该方法的FPGA硬件实现方法,包括图像数据缓冲单元、插值系数生成单元以及插值计算单元等。应用结果表明,双线性插值算法及其硬件实现模块达到了预期的效果。     

一种基于遗传算法的PID参数的优化控制策略

针对某一控制对象，通过数学推导，得出一组值Kp，K1，KD将其作为遗传算法的参考值。虽是随机产生初始群体，但可以预置大致范围，并在此基础上进行优化，可提高遗传算法的收敛速度。     

SSOR preconditioned CG method for the linear interference cancellation of asynchronous CDMA systems

An ideal computation of the decorrelating or the linear minimum mean-squared-error (LMMSE) detector requires computational complexity of order K ³ when there K is the number of users. To alleviate the computational complexity, iterative decorrelating and LMMSE detectors are proposed for solving a set of linear equations corresponding to linear interference cancellation structures. Iterative conjugate gradient (CG) method has been used for the linear interference cancellation detectors. Its main advantages are to reduce the order of computation complexity and their suitability to highly parallel implementations. In this paper, the symmetric successive overrelaxation (SSOR) preconditioning scheme is applied to the CG method. The performance of the detectors is investigated and it is found that the SSOR preconditioned CG method can provide significantly faster convergence than CG method.     

Preconditioned conjugate gradient methods for solving electromagnetic problems

It is shown that appropriately chosen preconditioners can significantly improve the convergence rate of the conjugate gradient (CG) algorithm as applied to electromagnetic problems. Preconditioners are constructed for the problems of scattering from frequency selective surfaces and scattering from infinite cylinders.     

Linear Interference Cancellation of Asynchronous CDMA Systems by Preconditioned CG Method

It is well known that the iterative method is used for solving a set of linear equations corresponding to linear interference cancellation structures. An ideal computation of the decorrelating or the linear minimum mean-squared-error (LMMSE) detector requires order K ³ flops, where K is the number of users. To alleviate the computational complexity, iterative decorrelating and the LMMSE detectors are proposed. In this paper, the symmetric successive over relaxation (SSOR) preconditioning scheme is applied to the conjugate gradient (CG) method. The performance of the detectors is investigated and it is found that the SSOR preconditioned CG (PCG) method can provide significantly faster convergence than CG method.     

Multipath reduction using constant modulus conjugate gradienttechniques

A conjugate-gradient (CG) constant-modulus adaptive processor is proposed. For the generalized sidelobe canceler (GSC) signal processing configuration, this algorithm, CG-GSC, exhibits improved convergence over previous methods. Theoretical expressions are presented for convergence and weight update of a linearly constrained constant modulus generalized sidelobe canceler. Theoretical expressions are then derived for the conjugate direction vectors. These vectors are used to update the filter weights for a conjugate gradient adaptation rule. A simulation study of the conjugate adaptation rule reveals the increase in convergence rate for the generalized sidelobe canceler. Performance comparisons of the CG-GSC and a first-order gradient GSC for a BPSK signal with multipath and white noise interference indicate that the CG-GSC adaptation rule not only increases convergence by a factor of five compared to the first-order gradient GSC, but in some instances improves the bit error rate of the demodulated BPSK signal     

基于混合PSO小波网络的网络异常检测

提出一种用新型的进化学习算法训练的小波神经网络(WNN).这种新型的进化学习算法是基于粒子群算法(PSO)和共轭下降法(CG)提出的.以往,将粒子群算法用于神经网络的训练一般是可行的.因为粒子群算法相比于其他的优化算法,具有相对简单的结构和快速的收敛速度,然而,由于粒子的搜索坍塌速度过快而导致粒子停滞这种潜在的危险.粒子的持续停滞使搜索结果很难达到全局最优,甚至会陷入局部最优.为了克服粒子群算法缺点提出了改进的混合算法.通过对KDD 99数据集的实验表明,利用新型混合算法训练的小波神经网络对于异常检测具有很高的异常检测率并且又较低的误判率.可见,该方法对于网络异常检测是有效的.