On convergence of the Horn and Schunck optical-flow estimation method

The purpose of this study is to prove convergence results for the Horn and Schunck optical-flow estimation method. Horn and Schunck stated optical-flow estimation as the minimization of a functional. When discretized, the corresponding Euler-Lagrange equations form a linear system of equations We write explicitly this system and order the equations in such a way that its matrix is symmetric positive definite. This property implies the convergence Gauss-Seidel iterative resolution method, but does not afford a conclusion on the convergence of the Jacobi method. However, we prove directly that this method also converges. We also show that the matrix of the linear system is block tridiagonal. The blockwise iterations corresponding to this block tridiagonal structure converge for both the Jacobi and the Gauss-Seidel methods, and the Gauss-Seidel method is faster than the (sequential) Jacobi method.     

An iterative method of solving a system of linear equations and its physical interpretation from the point of view of scattering theory

The iterative method is useful to find the approximate solution of large systems of linear equations when the exact method becomes too expensive to be implemented. One well-known iterative method is the Gauss-Seidel method. The author presents an alternative algorithm which has certain simplicity in its formulation. He uses the system of linear equations encountered in the theory of coupled antennas to illustrate this method and give a physical interpretation of the successive approximations from the point of view of scattering theory. A simple numerical example is given to compare the products resulting from this method and those obtained by the Gauss-Seidel method     

TWO-DIMENSION ITERATIVE METHOD——A UNIFIED APPROACH FOR SOLVING LINEAR EQUATIONS

In this paper, a unified approach of iterative methods, such as Jacobi method, Gauss-Seidel method, and SOR method, for solving linear equations is discussed and studied. For the reason stated in this paper, this approach is called the two-dimension iterative method. The convergence range and the rate of convergence of iteration process are improved by using this new approach. The theoretical analysis and the computing results demonstrate that this approach has many advantages over the generally used iterative methods. It is useful in solving large scale electric circuits, such as VLSI.     

求解线性方程组的迭代法的统一二维迭代法

求解线性方程组Ax=b的迭代法有其独特的实用意义,但由于其收敛的问题而受到限制。本文导出了常用的雅各比法、高斯-塞德尔法和逐次超松弛法等的统一方法,称之为二维迭代法,并由此得到了从新的角度改进迭代法的收敛性和收敛速度的途径。理论分析和数值计算都表明该方法优于常用的迭代法。此方法在解大规模电路中有用,例如用于VLSI的模拟。     

Iterative multiuser detection with Gauss-Seidel soft detector asfirst stage for asynchronous coded CDMA

A new iterative detection and decoding structure for asynchronous convolutionally coded and turbo coded CDMA is proposed. The new scheme is based on the combination of Gauss-Seidel soft detection and parallel interference cancellation. The complexity of the new scheme is linear to the number of users. It is shown that for a heavily loaded system, near-optimal performance can be obtained     

三维柱坐标下ADI-WLP FDTD算法的CPML实现

提出一种三维柱坐标系下交变方向隐式(ADI)的加权拉盖尔时域有限差分(WLP-FDTD)算法,并利用卷积完全匹配层(CPML)实现。通过引入微扰项可将大型稀疏矩阵的CPML 形式分解为6个三对角矩阵,之后结合高斯-赛德尔思想,将6 个三对角矩阵划分为两部分迭代计算,可进一步提升计算效率和收敛速度。在柱坐标模型的应用算例中,数值计算结果显示该算法的CPML 吸收边界对比Mur 吸收边界有较好的吸收效果。     

基于SWCoSaMP算法的稀疏信号重构

压缩感知(compressed sensing, CS)稀疏信号重构本质上是在稀疏约束条件下求解欠定方程组。针对压缩感知匹配追踪(compressed sampling matching pursuit, CoSaMP)算法直接从代理信号中选取非零元素个数两倍作为支撑集,但是不存在迭代量化标准,本文提出了分步压缩感知匹配追踪(stepwise compressed sampling matching pursuit, SWCoSaMP)算法。该算法从块矩阵的逆矩阵定义出发,采用迭代算法得到稀疏信号的支撑集,推出每次迭代支撑集所对应重构误差的L-2范数闭合表达式,从而重构稀疏信号。实验结果表明和原来CoSaMP算法相比,对于非零元素幅度服从均匀分布和高斯分布的稀疏信号,新算法具有更好的重构效果。      

求解稀疏最小二乘问题的新型Bregman迭代正则化算法

由于允许从少量数据中恢复原始图像或信号的压缩感知的引入,基于l1范数正则化的最优化方法近来越来越受到重视。利用最小二乘问题的一种等价形式和Bregman迭代方法的一些技巧,本文给出了已有A^+线性Bregman迭代方法的一种推导过程。进一步结合不动点连续迭代方法非满值最小二乘问题的等价形式,获得了一种求解带有约束的l1范数最小优化问题的新型算法,并给出了新型算法与A^+线性Bregman迭代算法之间的联系,同时证明了新算法所获得的解是所求问题的一个最优解。新算法与已有A^+算法类似,仅仅需要矩阵向量乘法和压缩算子的计算,从而使得新的算法很容易实现,且运算速度明显快于已有算法。最后,通过数值实验表明,新方法对于稀疏信号的恢复问题与原方法比具有速度快、可有效减少停滞现象等优点。      

基于稀疏贝叶斯学习的双基雷达关联成像

双基雷达具有隐蔽性高、抗干扰性能强等优点,在现代电子战中发挥重要作用。基于雷达关联成像原理,该文研究运动目标双基雷达关联成像问题。首先,针对采用均匀线性阵列作为收发天线的双基雷达系统,在发射随机频率调制信号条件下,分析运动目标雷达回波信号特点,建立双基雷达关联成像参数化稀疏表征模型;其次,针对建立的参数化稀疏表征模型,提出一种基于稀疏贝叶斯学习的迭代关联成像算法。该算法在建立贝叶斯模型基础上,通过贝叶斯推理,得到稀疏重构信号,从而实现对运动目标成像和运动参数的精确估计。最后,通过仿真实验验证所提方法的有效性。     

稀疏信道下基于稀疏贝叶斯学习的精简星座盲均衡算法

针对稀疏信道的盲均衡问题,在精简星座均衡算法框架下建立线性模型,利用稀疏信道下均衡器固有的稀疏特性,引入具有稀疏促进作用的先验分布对均衡器系数加以约束,使用稀疏贝叶斯学习方法迭代求解均衡器系数得到最大后验估计值。该文提出的均衡方法属于数据复用类均衡算法的范畴,能够适用于数据较短的应用场合。与随机梯度方法相比,算法性能受均衡器长度影响较小,收敛后误符号率性能更好,仿真实验验证了算法的有效性。     

OFDM系统在循环前缀不足时的两种高效迭代均衡方法

本文提出两种新的用于循环前缀(CP)不足时正交频分复用(OFDM)系统的迭代均衡方法。首先,我们提出并行迭代均衡(PIE)方法,该方法分别使用时域判决反馈方法和频域并行迭代方法来消除符号间干扰(ISI)和子载频间干扰(ICI)。为了改进PIE的性能,提出基于高斯-塞德尔迭代的串行迭代均衡(SIE)方法。在不增加计算复杂度的情况下,SIE具有比PIE更快的收敛速度。仿真结果表明,新方法可以在几次迭代后得到接近CP足够情况下的系统性能,PIE的性能与传统的迭代干扰消除方法相同,而SIE则提供好得多的收敛性能。     

Regularized MSBL algorithm with spatial correlation for sparse hyperspectral unmixing

Sparse unmixing is a promising approach that is formulated as a linear regression problem by assuming that observed signatures can be expressed as a linear combination of a few endmembers in the spectral library. Under this formulation, a novel regularized multiple sparse Bayesian learning model, which is constructed via Bayesian inference with the conditional posterior distributions of model parameters under a hierarchical Bayesian model, is proposed to solve the sparse unmixing problem. Then, the total variation regularization and the non-negativity constraint are incorporated into the model, thus exploiting the spatial information and the physical property in hyperspectral images. The optimal problem of the model is decomposed into several simpler iterative optimization problems that are solved via the alternating direction method of multipliers, and the model parameters are updated adaptively from the algorithm. Experimental results on both synthetic and real hyperspectral data demonstrate that the proposed method outperforms the other algorithms.     

A New Linear Group-Wise SIC Multiuser Detector

In this work, we introduce a new linear group-wise SIC multi-user detector that can converge to either the decorrelator or the least minimum mean-square error (LMMSE) detector. We study the convergence behavior of the proposed scheme and show that the latter is equivalent to the block Gauss-Seidel iterative method if the group-detection scheme used is the decorrelator detector. Moreover, we prove that the latter is convergent if the group-detection matrix is positive definite. Our simulation results are in excellent agreement with the proposed theory     

大规模MIMO系统低复杂度混合迭代信号检测

在大规模MIMO系统上行链路信号检测算法中,最小均方误差(MMSE)算法能获得接近最优的线性检测性能.但是,传统的MMSE检测算法涉及高维矩阵求逆运算,由于复杂度过高而使其在实际应用中难以快速有效地实现.基于最速下降(steepest descent,SD)算法和高斯一赛德尔(Gauss-Seidel,GS)迭代的方法提出了一种低复杂度的混合迭代算法,利用SD算法为复杂度相对较低的GS迭代算法提供有效的搜索方向,以加快算法收敛的速度.同时,给出了一种用于信道译码的比特似然比(LLR)近似计算方法.仿真结果表明,通过几次迭代,给出的算法能够快速收敛并接近MMSE检测性能,并将算法复杂度降低一个数量级,保持在O(K2).     

改进的稀疏近似逆预条件算法求解电磁场边值问题

提出了一种MAINV稀疏近似逆预条件算法,用于改善电磁场边值问题的有限元分析所产生的的线性系统的迭代求解。该预条件子是在基本AINV算法基础上,在分解过程中对可能导致算法崩溃的极小主元进行实时补偿,从而获得高质量的预条件子。数值结果表明,MAINV预条件子对SQMR以及若干经典迭代法的加速效果十分明显;此外,与其他常规预条件子相比较,MAINV具有更好的求解性能。     

基于DSP + FPGA的红外焦平面像素倍增技术

文章讨论了非制冷红外热像系统的总体性能,分析了影响该热像仪综合性能的主要原因,提出性能改善的基本方法,介绍了独特的虚拟电子微扫技术的基本原理及实现方法。针对远处小目标红外图像的有用信息进行了放大处理。采用DSP + FPGA的架构在硬件平台上得到了实现。实验证明:虚拟电子微扫技术有利于识别目标,效果良好。     

Efficient linear system solution in moment methods using wavelet expansions

An efficient strategy is proposed to solve linear systems encountered when method of moments (MoM) and wavelet expansions are used. It exploits a high-performance matrix bandwidth reduction algorithm so that it can be taken advantage of direct banded solvers, which have a more favorable computational complexity with respect to the typically used iterative sparse methods. Speedups of up to seven have been experienced with respect to standard iterative sparse solvers.     

衍射层析模型下穿墙雷达三维学习成像方法

针对现有穿墙雷达三维稀疏成像中,存在网格时延构建字典矩阵所需内存过大以及凸优化稀疏成像算法阈值参数不确定影响重建图像质量的问题,提出了一种基于衍射层析稀疏模型的学习近似消息传递三维成像方法。该方法在衍射层析成像算法上通过构造快速傅里叶变换算子来建立三维成像稀疏模型,然后修正近似消息传递算法求解稀疏解,并将其迭代过程映射成多层神经网络,最后通过数据驱动自适应学习多层神经网络中的可调参数,从而实现三维学习成像。仿真和实验数据处理结果表明,该方法不仅减小了系统所需内存,还避免了参数的人工调整对成像质量的影响。     

Krylov space methods on state-space control models

We give an overview of various Lanczos/Krylov space methods and the way in which they are being used for solving certain problems in Control Systems Theory based on state-space models. The matrix methods used are based on Krylov sequences and are closely related to modern iterative methods for standard matrix problems such as sets of linear equations and eigenvalue calculations. We show how these methods can be applied to problems in Control Theory such as controllability, observability, and model reduction. All the methods are based on the use of state-space models, which may be very sparse and of high dimensionality. For example, we show how one may compute an approximate solution to a Lyapunov equation arising from a discrete-time linear dynamic system with a large sparse system matrix by the use of the Arnoldi algorithm, and so obtain an approximate Gramian matrix. This has applications in model reduction. The close relation between the matrix Lanczos algorithm and the algebraic structure of linear control systems is also explored.     

An Iterative Bayesian Algorithm for Sparse Component Analysis in Presence of Noise

We present a Bayesian approach for sparse component analysis (SCA) in the noisy case. The algorithm is essentially a method for obtaining sufficiently sparse solutions of underdetermined systems of linear equations with additive Gaussian noise. In general, an underdetermined system of linear equations has infinitely many solutions. However, it has been shown that sufficiently sparse solutions can be uniquely identified. Our main objective is to find this unique solution. Our method is based on a novel estimation of source parameters and maximum a posteriori (MAP) estimation of sources. To tackle the great complexity of the MAP algorithm (when the number of sources and mixtures become large), we propose an iterative Bayesian algorithm (IBA). This IBA algorithm is based on the MAP estimation of sources, too, but optimized with a steepest-ascent method. The convergence analysis of the IBA algorithm and its convergence to true global maximum are also proved. Simulation results show that the performance achieved by the IBA algorithm is among the best, while its complexity is rather high in comparison to other algorithms. Simulation results also show the low sensitivity of the IBA algorithm to its simulation parameters.