Orthogonal, exactly periodic subspace decomposition

The detection and estimation of machine vibration multiperiodic signals of unknown periods in white Gaussian noise is investigated. New estimates for the subsignals (signals making up the received signal) and their periods are derived using an orthogonal subspace decomposition approach. The concept of exactly periodic signals is introduced. This in turn simplifies and enhances the understanding of periodic signals.     

Fast LV motion estimation using subspace approximation techniques

Cardiac motion estimation is very important in understanding cardiac dynamics and in noninvasive diagnosis of heart disease. Magnetic resonance (MR) imaging tagging is a technique for measuring heart deformations. In cardiac tagged MR images, a set of dark lines are noninvasively encoded within myocardial tissue providing the means for measurement of deformations of the heart. The points along tag lines measured in different frames and in different directions carry important information for determining the three-dimensional nonrigid movement of left ventricle. However, these measurements are sparse and, therefore, multidimensional interpolation techniques are needed to reconstruct a dense displacement field. In this paper, a novel subspace approximation technique is used to accomplish this task. We formulate the displacement estimation as a variational problem and then project the solution into spline subspaces. Efficient numerical methods are derived by taking advantages of B-spline properties. The proposed technique significantly improves our previous results reported in [3] with respect to computational time. The method is applied to a temporal sequence of two-dimensional images and is validated with simulated and in vivo heart data.     

基于子空间分解的多通道盲解卷积算法

针对卷积混合信号,提出了一种新的多通道盲解卷积算法,该算法首先利用子空间分解方法,将信号卷积混合模型变换成线性混合模型,然后利用线性混合盲分离算法分离出源信号.该算法相对频域盲解卷积算法来说无需解决线性混合盲分离中存在的幅度和排列顺序的模糊性问题,而且该算法不要求信号独立同分布,只要求各源信号统计独立即可.因此,该算法可以直接在中频对观察信号进行处理.计算机仿真结果表明,该算法不仅能对不同频不同调制方式的通信信号进行盲解卷积,而且对同频同调制的通信信号,该算法同样有效.     

基于子空间分解的OFDM信道盲辨识

该文提出一种基于子空间分解的正交频分复用(OFDM)信道的盲辨识算法,将OFDM信号等效为单输入多输出的过采样信号,采用过采样信号的循环稳态特性和子空间分解方法估计信道参数,算法不需要任何训练序列和周期性的引导信号,实现了0FDM信道的盲辨识。对于宽带OFDM移动通信系统,通常子信道数较大,信道响应持续时间短于0FDM符号周期,因此,可以将整个系统分为若干个子系统,各子系统分别进行信道辨识,能有效地降低信道估算的复杂性。     

子空间分解方法在语音增强系统中的应用

介绍了基于子空间分解的单通道语音增强的方法，并利用有声/无声检测的判决算法提高了对噪声估计的准确度，通过KL展开将含噪语音分解为信号子空间和噪声子空间，并在信号子空间中对原始语音信号进行了最优的估计，有效地滤除了数字语音系统中的宽带噪声，并在一定程度上抑制了“音乐噪声”的影响，获得了较好的语音增强效果。     

Blind MIMO system identification based on cumulant subspace decomposition

Blind identification of multiple-input multiple-output (MIMO) linear systems can be achieved by utilizing higher order statistics of the output signals. We study the blind identification of MIMO systems whose inputs are mutually independent, temporally white, non-Gaussian source signals. Based on sub-space analysis, we develop a new linear batch algorithm to identify MIMO systems from the common space of a set of fourth-order cumulant matrices of the channel outputs. Given knowledge of the channel orders, the identifiability conditions required by the proposed algorithm are properly established. Like most subspace-based approaches, this new algorithm remains sensitive to channel order overestimation. Simulation results illustrate its performance for various channel models.     

Perturbation analysis for subspace decomposition with applications in subspace-based algorithms

Subspace decomposition has been exploited in different applications. Due to perturbations from various sources such as finite data samples and measurement noise, perturbations arise in subspaces. Therefore, some loss is introduced to performance of subspace-based algorithms. Although first-order perturbation results have been proposed in the literature and applied to various problems, up to second-order perturbation analysis can provide more accurate analytical results and is studied in this paper. Based on the orthogonality principle, perturbations of subspaces and singular values (or eigenvalues) are derived explicitly as functions of a perturbation in the objective matrix up to the second-order, respectively, all in closed forms. It is shown that by keeping only the first-order terms, the derived results reduce to those from existing approaches. Examples to apply the proposed results to both matrix computation and subspace-based channel estimation are provided to verify our analysis.     

Delay correlation subspace decomposition algorithm and its application in fMRI

This paper reports a new delay subspace decomposition (DSD) algorithm. Instead of using the canonical zero-delay correlation matrix, the new DSD algorithm introduces a delay into the correlation matrix of the subspace decomposition to suppress noises in the data. The algorithm is applied to functional magnetic resonance imaging (fMRI) to detect the regions of focal activities in the brain. The efficiency is evaluated by comparing with independent component analysis and principal component analysis method of fMRI.     

MTI雷达中基于子空间分解的杂波抑制算法

最优MTI滤波器的权值与目标的多普勒频率有关，传统的MTI雷达需要利用一组能覆盖目标多普勒频率范围的并行滤波器组来实现最佳滤波。本文提出了一种算法，通过子空间分解法直接求取滤波器的权系数，由于无需多普勒滤波器组，系统的复杂度得到了降低。为了适应杂波的变化，本文还推导了该算法基于幂迭代的自适应过程。仿真结果表明：在不同的杂波环境下，该算法均有良好的MTI改善因子。     

Speckle filtering in polarimetric SAR data based on the subspace decomposition

In this paper, a new approach to speckle filtering of synthetic aperture radar (SAR) data is presented. We define a parameter space consisting of two orthogonal subspaces-the signal subspace and the noise subspace. Then, the full polarimetric information from the signal subspace is obtained after speckle filtering. In this way, edges of different kinds of targets are preserved. The effectiveness of this method is demonstrated using the National Aeronautics and Space Administration Jet Propulsion Laboratory airborne L-band polarimetric SAR data.     

链接文档中基于子空间分解的高效谱聚类算法

提出了一种基于子空间分解的高效谱聚类算法。首先,基于共识信息和特定域信息的矩阵分解将链接文档划分为3个子空间,然后对子空间添加正则化项建模共识信息和特定域信息对聚类的不同影响,并采用交替优化方法实现谱聚类。考虑到谱聚类的复杂性,提出了一种带曲线搜索的梯度下降法加速求解过程。3个真实数据集上的实验结果表明,所提算法在聚类质量和效率方面始终明显优于目前典型的基线算法,且对输入参数不敏感。     

Fast eigenspace decomposition of correlated images

We present a computationally efficient algorithm for the eigenspace decomposition of correlated images. Our approach is motivated by the fact that for a planar rotation of a two-dimensional (2-D) image, analytical expressions can be given for the eigendecomposition, based on the theory of circulant matrices. These analytical expressions turn out to be good first approximations of the eigendecomposition, even for three-dimensional (3-D) objects rotated about a single axis. In addition, the theory of circulant matrices yields good approximations to the eigendecomposition for images that result when objects are translated and scaled. We use these observations to automatically determine the dimension of the subspace required to represent an image with a guaranteed user-specified accuracy, as well as to quickly compute a basis for the subspace. Examples show that the algorithm performs very well on a number of test cases ranging from images of 3-D objects rotated about a single axis to arbitrary video sequences.     

Fast subspace tracking and neural network learning by a novelinformation criterion

We introduce a novel information criterion (NIC) for searching for the optimum weights of a two-layer linear neural network (NN). The NIC exhibits a single global maximum attained if and only if the weights span the (desired) principal subspace of a covariance matrix. The other stationary points of the NIC are (unstable) saddle points. We develop an adaptive algorithm based on the NIC for estimating and tracking the principal subspace of a vector sequence. The NIC algorithm provides a fast on-line learning of the optimum weights for the two-layer linear NN. We establish the connections between the NIC algorithm and the conventional mean-square-error (MSE) based algorithms such as Oja's algorithm (Oja 1989), LMSER, PAST, APEX, and GHA. The NIC algorithm has several key advantages such as faster convergence, which is illustrated through analysis and simulation     

Cognitive radio signal classification based on subspace decomposition and RBF neural networks

Spectrum sensing is one of the major challenges for commercial development of cognitive radio systems, since the detection of the presence of a primary user is a complex task that requires high reliability. This work proposes a signal classifier capable of detecting and identifying a primary user signal on a given channel of the radio spectrum. The proposed approach combines eigen-decomposition techniques and neural networks not only to decide about the presence of a primary user, but also to identify the primary user signal type, a feature that is not encountered in the current approaches proposed in literature. Besides the advantage of identifying the primary user type, the proposed method also considerably reduces the computational cost of the detection process. The proposed classification method has been applied to the development of five primary user signal Classification Modules, which includes wireless microphone, orthogonal frequency-division multiplexing and Digital Video Broadcasting-Terrestrial signals. The results show that the proposed classifier correctly detects and identifies the primary users, even under low signal to noise ratio and multipath scenarios.     

基于奇异值分解的快速直线提取方法

矩阵的奇异值分解能够反映矩阵数据的分布特征.利用数字图像中直线的结构特征,定义了近垂直直线基元和近水平直线基元,根据基元结构对边缘检测和细化后得到的线段进行扫描,将近似共线的点分别归入到若干个直线支撑点集合.对每个直线支撑点集合进行奇异值分解,利用得到的特征向量计算出其对应的Hough参数空间投票单元,实现对线段层次上...     

Fast and scalable parallel layout decomposition in double patterning lithography

For 32/22 nm technology nodes and below, double patterning (DP) lithography has become the most promising interim solutions due to the delay in the deployment of next generation lithography (e.g., EUV). DP requires the partitioning of the layout patterns into two different masks, a procedure called layout decomposition. Layout decomposition is a key computational step that is necessary for double patterning technology. Existing works on layout decomposition are all single-threaded, which is not scalable in runtime and/or memory for large industrial layouts. This paper presents the first window-based parallel layout decomposition methods for improving both runtime and memory consumption. Experimental results are promising and show the presented parallel layout decomposition methods obtain upto 21× speedup in runtime and upto 7.5×reduction in peak memory consumption with acceptable solution quality.     

基于PSO和LM的信号稀疏分解快速算法

传感矩阵和重建算法的性能分析和优化是目前压缩传感领域研究的热点。针对匹配追踪算法在信号稀疏分解中计算量巨大的难题,提出了一种交替使用粒子群算法和LevenbergMarquardt算法的混合智能算法来寻找最佳原子。首先利用粒子群算法得到群体最优解,再以该解作为LM算法的初值,交替使用两种算法,直至发现满意的最优解。数值分析表明,新算法克服了粒子群算法过早收敛于局部极值和LM算法依赖初值的问题,保证了求解的速度和精度。     

Fast prime factor decomposition algorithms for a family of discrete trigonometric transforms

This paper develops a set of fast prime factor decomposition algorithms (PFDAs) for a family of discrete trigonometric transforms of sizeN, whereN is a product of two relatively prime integers. Relevant equations for the PFDAs are derived. Computational procedures are presented followed by a specific example forN= 12. The input and output index mappings necessary for the algorithm are obtained and the computational complexity is briefly outlined.This research was supported by NSERC.Visiting scholar on leave of absence from Department of Radio and Electronics, Anhui University, Anhui, People's Republic of China.     

Matched subspace detectors

We formulate a general class of problems for detecting subspace signals in subspace interference and broadband noise. We derive the generalized likelihood ratio (GLR) for each problem in the class. We then establish the invariances for the GLR and argue that these are the natural invariances for the problem. In each case, the GLR is a maximal invariant statistic, and the distribution of the maximal invariant statistic is monotone. This means that the GLR test (GLRT) is the uniformly most powerful invariant detector. We illustrate the utility of this finding by solving a number of problems for detecting subspace signals in subspace interference and broadband noise. In each case we give the distribution for the detector and compute performance curves