采用奇异值分解方法的半盲信道辨识算法

针对全盲信道辨识算法无法辨识含公零点信道且对信道阶数误差敏感的问题,提出一种半盲信道辨识算法。通过奇异值分解将信道矩阵分解为同维矩阵与酉矩阵乘积的形式,分别利用接收数据和已知符号求解同维矩阵与酉矩阵,最终得到信道矩阵的闭式解。该算法有效地克服了全盲信道辨识算法的诸多局限性,避免了传统半盲方法面临的最优加权选择问题,性能稳定,且对信道噪声与信道阶数都具有较强的鲁棒性。仿真实验验证了所提算法的有效性与优越性。     

基于奇异值分解的自适应模板更新研究

研究了基于奇异值分解的图像匹配和目标跟踪问题。由于图像的奇异值特征具有良好的稳定性,可以将奇异值当作一种有效的代数特征来描述并表征图像。根据所定义的奇异值缩放不变量提出了一种基于奇异值分解的模板更新算法。在算法中,根据奇异值向量的缩放不变特征来度量当前模板内的目标信息,然后根据所定义的置信度自动计算更新后所需的模板大小,从而使更新后的模板更有效地包含目标。试验表明：提出的模板更新算法在序列图像的目标跟踪中具有较好的实用性。     

基于关联规则与奇异值分解的音乐推荐系统

在音乐推荐系统中引入了关联规则和奇异值分解两种算法。通过分析数据集得到语义词汇间的强关联规则,用来扩展能够描述歌曲典型特征的语义词汇集。根据歌曲与语义词汇集的关联程度,计算歌曲间相似度,获取推荐列表。应用SVD算法对数据集进行降维,在低维语义空间中找到能够代表歌曲的特征,利用这些特征计算歌曲间相似度,获取推荐列表。本文实现了两种算法并对比了推荐效果,为音乐推荐系统效果提升做了有益探索。     

基于奇异值分解的光电跟踪系统标定方法

针对地面光电跟踪系统的误差定位进行了理论分析,确定影响其目标定位精度的误差因素主要是垂直度误差、零位误差、基座安装误差等,给出了光电跟踪系统的标定流程。利用标定过程中坐标变换的顺序特性,通过奇异值分解原理给出了坐标变换的变换矩阵,包括平移矩阵、旋转矩阵及其欧拉角;同时通过标定流程的迭代,确定了固定俯仰偏移角度的大小。最后通过试验验证了此标定流程的准确性。     

Saliency detection based on singular value decomposition

Saliency detection has gained popularity in many applications, and many different approaches have been proposed. In this paper, we propose a new approach based on singular value decomposition (SVD) for saliency detection. Our algorithm considers both the human-perception mechanism and the relationship between the singular values of an image decomposed by SVD and its salient regions. The key concept of our proposed algorithms is based on the fact that salient regions are the important parts of an image. The singular values of an image are divided into three groups: large, intermediate, and small singular values. We propose the hypotheses that the large singular values mainly contain information about the non-salient background and slight information about the salient regions, while the intermediate singular values contain most or even all of the saliency information. The small singular values contain little or even none of the saliency information. These hypotheses are validated by experiments. By regularization based on the average information, regularization using the leading largest singular values or regularization based on machine learning, the salient regions will become more conspicuous. In our proposed approach, learning-based methods are proposed to improve the accuracy of detecting salient regions in images. Gaussian filters are also employed to enhance the saliency information. Experimental results prove that our methods based on SVD achieve superior performance compared to other state-of-the-art methods for human-eye fixations, as well as salient-object detection, in terms of the area under the receiver operating characteristic (ROC) curve (AUC) score, the linear correlation coefficient (CC) score, the normalized scan-path saliency (NSS) score, the F-measure score, and visual quality.     

The hyperbolic singular value decomposition and applications

A new generalization of the singular value decomposition (SVD), the hyperbolic SVD, is advanced, and its existence is established under mild restrictions. The hyperbolic SVD accurately and efficiently finds the eigenstructure of any matrix that is expressed as the difference of two matrix outer products. Signal processing applications where this task arises include the covariance differencing algorithm for bearing estimation in sensor arrays, sliding rectangular windowing, and array calibration. Two algorithms for effecting this decomposition are detailed. One is sequential and follows a similar pattern to the sequential bidiagonal based SVD algorithm. The other is for parallel implementation and mimics Hestenes' SVD algorithm (1958). Numerical examples demonstrate that like its conventional counterpart, the hyperbolic SVD exhibits superior numerical behavior relative to explicit formation and solution of the normal equations. Furthermore, the hyperbolic SVD applies in problems where the conventional SVD cannot be employed     

OFDM channel estimation by singular value decomposition

We present and analyze low-rank channel estimators for orthogonal frequency-division multiplexing (OFDM) systems using the frequency correlation of the channel. Low-rank approximations based on the discrete Fourier transform (DFT) have been proposed, but these suffer from poor performance when the channel is not sample spaced. We apply the theory of optimal rank-reduction to linear minimum mean-squared error (LMMSE) estimators and show that these estimators, when using a fixed design, are robust to changes in channel correlation and signal-to-noise ratio (SNR). The performance is presented in terms of uncoded symbol-error rate (SER) for a system using 16-quadrature amplitude modulation (QAM)     

基于奇异值分解的特征跟踪方法

在传统的基于模板匹配的跟踪方法中，均是给定一个模板，然后从图像中各个位置取出一个个与模板大小一致的区域进行相似性度量，找出与模板距离最小的一个区域作为当前模板，以便进行下一步的匹配跟踪工作。在景象匹配和相关跟踪过程中，由于所面临的大多数是变化的场景，实时获取的图像与预存模板之间存在比较大的差异，传统相关匹配方法的应用就会受到限制；而且在跟踪过程中，随时更新模板会造成跟踪性能对扰动过分敏感，从而产生漂移。首先拍摄目标不同角度的图像（尽可能包含目标可能出现的所有情况），构成目标图像训练集合，抽取出特征矩阵，对它进行奇异值分解，构成一个关于目标的多维空间。然后再用匹配方法在全局范围搜索，找出目标的大致位置，并利用收敛方法在确定的大致位置内进行搜索，确定目标的仿射变换系数，从而得到一个目标位置的确切描述。     

Subspace-based signal analysis using singular value decomposition

A unified approach is presented to the related problems of recovering signal parameters from noisy observations and identifying linear system model parameters from observed input/output signals, both using singular value decomposition (SVD) techniques. Both known and new SVD-based identification methods are classified in a subspace-oriented scheme. The SVD of a matrix constructed from the observed signal data provides the key step in a robust discrimination between desired signals and disturbing signals in terms of signal and noise subspaces. The methods that are presented are distinguished by the way in which the subspaces are determined and how the signal or system model parameters are extracted from these subspaces. Typical examples, such as the direction-of-arrival problem and system identification from input/output measurements, are elaborated upon, and some extensions to time-varying systems are given     

基于高维张量奇异值分解的图像加密

现有基于奇异值分解(SVD)的彩色信息加密系统提供了一种光学矩阵分解方案、安全的密文和敏感的密钥。高维张量奇异值分解(HOSVD)是SVD矩阵的自然线性延伸,提出了一种基于HOSVD的彩色图像加密算法。在加密过程中,HOSVD比SVD提供了更多的密文乘法组合次序。这些乘法组合次序可以有效地增加未经授权的解密难度。在解密过程中,HOSVD的重建精度比SVD更高。这些优点提高了准确性、安全性和鲁棒性。通过对100个图像测试数据集的计算机仿真验证了该算法的可行性。     

ECG data compression using truncated singular value decomposition

The method of truncated singular value decomposition (SVD) is proposed for electrocardiogram (ECG) data compression. The signal decomposition capability of SVD is exploited to extract the significant feature components of the ECG by decomposing the ECG into a set of basic patterns with associated scaling factors. The signal information is mostly concentrated within a certain number of singular values with related singular vectors due to the strong interbeat correlation among ECG cycles. Therefore, only the relevant parts of the singular triplets need to be retained as the compressed data for retrieving the original signals. The insignificant overhead can be truncated to eliminate the redundancy of ECG data compression. The Massachusetts Institute of Technology-Beth Israel Hospital arrhythmia database was applied to evaluate the compression performance and recoverability in the retrieved ECG signals. The approximate achievement was presented with an average data rate of 143.2 b/s with a relatively low reconstructed error. These results showed that the truncated SVD method can provide efficient coding with high-compression ratios. The computational efficiency of the SVD method in comparing with other techniques demonstrated the method as an effective technique for ECG data storage or signals transmission     

基于奇异值分解的图像目标跟踪算法

传统相关跟踪方法是利用模板图像与目标图像对应像素的灰度差异信息进行跟踪,它对旋转变化敏感,且存在跟踪累积误差,容易导致模板漂移而丢失目标。文中提出基于奇异值分解的跟踪算法,算法首先建立模板图像训练集合,利用奇异值分解方法,张成模板图像特征空间,然后求出模板图像在特征空间里的投影值,代替传统算法中灰度对两幅待匹配图像进行的全局搜索定位。在进行投影值间的相似性度量时,欧氏距离同等对待所有的特征向量不移合理,文中采用了一种鲁棒估计方法,可以对不同距离的值做不同处理。匹配跟踪实验效果良好。     

Image fusion using higher order singular value decomposition

A novel higher order singular value decomposition (HOSVD)-based image fusion algorithm is proposed. The key points are given as follows: 1) Since image fusion depends on local information of source images, the proposed algorithm picks out informative image patches of source images to constitute the fused image by processing the divided subtensors rather than the whole tensor; 2) the sum of absolute values of the coefficients (SAVC) from HOSVD of subtensors is employed for activity-level measurement to evaluate the quality of the related image patch; and 3) a novel sigmoid-function-like coefficient-combining scheme is applied to construct the fused result. Experimental results show that the proposed algorithm is an alternative image fusion approach.     

基于奇异值分解的图像匹配方法

传统的图像匹配方法中, 由于实时图和参考图之间存在着灰度差异和几何形变,仅用灰度作为特征进行匹配算法的性能很容易受到影响。文中提出了一种基于奇异值分解的图像匹配方法。该方法首先利用奇异值分解方法,求出模板图像矩阵的奇异值及奇异值向量,用它们作为模板图像的特征代替传统算法中的灰度对两幅待匹配图像进行全局搜索定位。由于奇异分解方法所特有的优越性,匹配实验取得了良好效果。实验结果验证了该方法的有效性。     

超分辨测向中奇异值分解的FPGA实现

奇异值分解是超分辨测向技术的核心组成部分,现有的并行实现方案适用范围窄,运算量大,迭代时间长.为了满足测向接收机系统的高实时性需求,结合双边Jacobi算法的交换策略和单边Jacobi算法的求角结构,提出了一种改进的实现方法.该实现方法修正了脉动阵列的收敛性问题,提高了复数矩阵的收敛速度.同时,给出了算法的现场可编程门阵列(FPGA)实现结构.仿真结果证明该方案耗时在百微秒以内,能够应用于电子侦察设备.     

基于多分辨奇异值分解的多聚焦图像融合

提出了一种多分辨奇异值分解（MSVD）的新框架,并把它应用于多聚焦图像融合中.首先,基于分块算法原理,利用奇异值分解获得具有不同分辨率的一幅近似和三幅细节图像.然后结合重构算法,给出了图像的融合框架.其次,对比基于离散小波变换（DWT）的融合算法,基于MSVD的融合效果更好,而且 MSVD的基向量只依赖于图像本身而不像小波需要固定的基.最后,采用客观性能指标对结果图像进行评价.实验结果表明,本文的方法不仅简单易行,而且图像表现出良好的视觉效果,清晰度和空间频率都有很大提高.     

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...     

Low-complexity video coding based on two-dimensional singular value decomposition

In this paper, we propose a low-complexity video coding scheme based upon 2-D singular value decomposition (2-D SVD), which exploits basic temporal correlation in visual signals without resorting to motion estimation (ME). By exploring the energy compaction property of 2-D SVD coefficient matrices, high coding efficiency is achieved. The proposed scheme is for the better compromise of computational complexity and temporal redundancy reduction, i.e., compared with the existing video coding methods. In addition, the problems caused by frame decoding dependence in hybrid video coding, such as unavailability of random access, are avoided. The comparison of the proposed 2-D SVD coding scheme with the existing relevant non-ME-based low-complexity codecs shows its advantages and potential in applications.     

迭代奇异值分解的学生成绩恢复方法

为了有效地对学生成绩数据进行恢复,提出一种迭代奇异值分解的学生成绩恢复方法。该方法采用矩阵表示学生成绩,利用该矩阵具有低秩的特性,在给定缺失元素的初始值后,利用奇异值分解得到缺失元素的近似值,而该近似值比初始值更加接近真实值。再将求到的近似值代替初始值,经过多次迭代,最终可求到成绩表中缺失元素的真实值。该方法的优点是在缺失元素恢复过程中,利用了所有已知元素信息,并将所有已知元素平等地对待。模拟实验和真实实验结果表明该方法能够快速、精确地恢复出学生的真实成绩。     

Parallel singular value decomposition of complex matrices usingmultidimensional CORDIC algorithms

The singular value decomposition (SVD) of complex matrices is computed in a highly parallel fashion on a square array of processors using Kogbetliantz's analog of Jacobi's eigenvalue decomposition method. To gain further speed, new algorithms for the basic SVD operations are proposed and their implementation as specialized processors is presented. The algorithms are 3-D and 4-D extensions of the CORDIC algorithm for plane rotations. When these extensions are used in concert with an additive decomposition of 2×2 complex matrices, which enhances parallelism, and with low resolution rotations early on in the SVD process, which reduce operation count, a fivefold speedup can be achieved over the fastest alternative approach