Sequential Unfolding SVD for Tensors With Applications in Array Signal Processing

This paper contributes to the field of higher order $(N>2)$ tensor decompositions in signal processing. A novel PARATREE tensor model is introduced, accompanied with Sequential Unfolding SVD (SUSVD) algorithm. SUSVD, as the name indicates, applies a matrix singular value decomposition sequentially on the unfolded tensor reshaped from the right hand basis vectors of the SVD of the previous mode. The consequent PARATREE model is related to the well known family of PARAFAC tensor decomposition models. Both of them describe a tensor as a sum of rank-1 tensors, but PARATREE has several advantages over PARAFAC, when it is applied as a lower rank approximation technique. PARATREE is orthogonal (due to SUSVD), fast and reliable to compute, and the order (or rank) of the decomposition can be adaptively adjusted. The low rank PARATREE approximation can be applied for, e.g., reducing computational complexity in inverse problems, measurement noise suppression as well as data compression. The benefits of the proposed algorithm are illustrated through application examples in signal processing in comparison to PARAFAC and HOSVD.      

An Efficient Way of Calculating Rotated Template Set Operators for Parallel Image Processing

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Variational Numerical Methods for Solving Nonlinear Diffusion Equations Arising in Image Processing

In this paper we give a general, robust, and efficient approach for numerical solutions of partial differential equations (PDEs) arising in image processing and computer vision. The well-established variational computational techniques, namely, finite element, finite volume, and complementary volume methods, are introduced on a common base to solve nonlinear problems in image multiscale analysis. Since they are based on principles like minimization of energy (finite element method) or conservation laws (finite and complemetary volume methods), they have strong physical backgrounds. They allow clear and physically meaningful derivation of difference equations that are local and easy to implement. The variational methods are combined with semi-implicit discretization in scale, which gives favorable stability and efficiency properties of computations. We show here L_∞-stability without any restrictions on scale steps. Our approach leads finally to solving linear systems in every discrete scale level, which can be done efficiently by fast preconditioned iterative solvers. We discuss such computational schemes for the regularized (in the sense of F. Catté et al., SIAM J. Numer. Anal.129, 1992, 182–193) Perona–Malik anisotropic diffusion equation (P. Perona and J. Malik, IEEE Trans. Pattern Anal. Mach. Intell.12, 1990, 629–639) and for nonlinear degenerate diffusion equation of mean curvature flow type studied by L. Alvarez et al. (SIAM J. Numer. Anal.129, 1992, 845–866).     

Rotated hyperbola model for smooth support vector machine for classification

This article puts forward a novel smooth rotated hyperbola model for support vector machine (RHSSVM) for classification. As is well known, the support vector machine (SVM) is based on statistical learning theory(SLT) and performs its high precision on data classification. However, the objective function is non-differentiable at the zero point. Therefore the fast algorithms cannot be used to train and test the SVM. To deal with it, the proposed method is based on the approximation property of the hyperbola to its asymptotic lines. Firstly, we describe the development of RHSSVM from the basic linear SVM optimization programming. Then we extend the linear model to non-linear model. We prove the solution of RHSSVM is convergent, unique, and global optimal. We show how RHSSVM can be practically implemented. At last, the theoretical analysis illustrates that compared with other three typical models, the rotated hyperbola model has the least error on approximating the plus function. Meanwhile, computer simulations show that the RHSSVM can reduce the consuming time at most 54.6% and can efficiently handle large scale and high dimensional programming.     

图像处理中扩散方程的快速数值解法

该文给出图像处理中常用的二阶非线性扩散方程的快速求解算法。首先提出一种线性差分离散格式,既包含了显格式,也包含了隐格式;其次给出了数值稳定性条件,最后讨论了3种快速解法：多重网格法(MG),交替方向隐格式(ADI),和加性算子分离格式(AOS)。对3种方法进行了比较和评价,结果表明：用3种方法得到的去噪效果基本相同;ADI和AOS实现较简单;多重网格法得到的恢复图像在光滑区域视觉上优于两种直接法。     

An Adaptive Finite Volume Scheme for Solving Nonlinear Diffusion Equations in Image Processing

We propose the coarsening strategy for the finite volume computational method given by K. Mikula and N. Ramarosy (Numer. Math.89, 2001, 561–590) for the numerical solution of the (modified in the sense of F. Catté et al. (SIAM J. Numer. Anal.29, 1992, 182–193)) Perona–Malik nonlinear image selective smoothing equation (called anisotropic diffusion in image processing). The adaptive aproach is directly at hand because a solution tends to be flat in large subregions of the image, and thus it is not necessary to consider the same fine resolution of computations in the whole spatial domain. This access reduces computational effort, because the coarsening of the computational grid rapidly reduces the number of unknowns in the linear systems to be solved at discrete scale steps of the method.     

复数域非线性扩散滤波在图像处理中的应用

图像处理中去噪和边缘保持是一对矛盾体,去噪滤波经常会失去高频部分的信号,而边缘信息主要以高频信息为主.考虑了一种新的方法——复数域非线性扩散方法,该方法通过结合自由薛定谔方程将传统各向异性扩散方程拓展到复数域,复数域实部信号可以很好地滤波,将复数域扩散项虚部加入shock滤波器,该方法克服了传统的边缘检测方法边缘保持能力差的缺点.试验结果表明:该算法具有良好的抗噪性和边缘细节的保持性,边缘检测效果良好.     

基于DVB-T2的旋转星座解映射算法及其改进

在广播和通信领域最新概念中,星座旋转作为一种分集技术被应用于DVB-T2标准。对于旋转星座采用基于硬判决的二维迭代LLR解映射算法进行了一些简化,但由于硬判决带来了误码传播,并且首次软信息计算仍较为复杂。提出了两种改进方案,分别从误码性能和运算复杂度方面对原算法进行了改进。仿真结果表明,信道条件较为恶劣时,改进方法在性能上优于原系统。     

Sphere Lower Bound for Rotated Lattice Constellations in Fading Channels

We study the error probability performance of rotated lattice constellations in frequency-flat Nakagami-m block-fading channels. In particular, we use the sphere lower bound on the underlying infinite lattice as a performance benchmark. We show that the sphere lower bound has full diversity. We observe that optimally rotated lattices with largest known minimum product distance perform very close to the lower bound, while the ensemble of random rotations is shown to lack diversity and perform far from it.     

两阶段平移、旋转图像高精度配准算法

图像配准在图像处理中是十分重要的,通常是许多现代图像处理和计算机视觉任务一个关键的预处理步骤,许多算法和技术已经被提出用来解决配准问题.本文提出一种稳健的两阶段层次配准算法,在频域组合相位相关和谱对消技术对平移和旋转图像获得亚像素精度的配准.算法第一阶段首先利用一维FFT技术实现图像的旋转以确定旋转角度,并利用这个旋转角度将两幅图像之间的运动简化为平移运动,然后利用相位相关法确定整数像素平移参数.算法第二阶段运用谱对消技术确定亚像素平移参数.提出的算法甚至在图像因为下采样而包含混淆误差情况下仍然能够获得亚像素精度配准.     

NGB-W系统中基于星座旋转的BICM的实现与性能分析

下一代无线广播网(Next Generation Broadcast-Wireless,NGB-W)中,利用复平面星座点的星座旋转以及星座点的同相分量与正交分量的交织,提出了一种更为有效的比特交织编码调制(Bit Interleaved Coded Modulation,BICM)技术方案.发送端采用这种比特交织编码调制技术,接收端可以通过引入信号空间分集来提升系统性能.仿真结果表明:由星座旋转带来的系统性能增益随信道的不同、调制阶数的不同以及LDPC编码率的不同而产生差异.     

比例误差扩散算法在数字图像处理中的应用

数字图像可看成是一个二维数组,是便于计算机处理的一种图像的表示形式。因此它是离散、量化的灰度-像素的集合。针对不同的图像成像存在的问题,采用不同的算法对二维函数进行处理,能得到一组新的不同的灰度-像素的集合,基于MATLAB的数字图像处理技术目前在电子成像及视频设备领域中有着广泛的应用。例如LED显示器中,采用一种基于MATLAB技术的比例误差扩散算法对数字图像进行处理,大大改善了图像的成像及显示的质量。     

A Rate-1 Space-Time Diversity Method for Rotated 4-QAM Constellations

We propose a rate-1 space-time transmit diversity technique. We obtained second-order diversity by transmitting the real and imaginary parts of the symbols from two antennas. With four transmit antennas, we can add Alamouti coding to reach fourth-order transmit diversity. There is no need to detect symbols jointly in either of these applications. It is possible to use both Alamouti coding and Hadamard spreading diversity with the proposed method, thereby obtaining eighth-order (or even higher) transmit diversity. However, joint detection of the symbols is again required at this point. The proposed technique is a suitable space-frequency coding method for OFDM systems. We used computer simulations to compare our technique with the Alamouti coding, quasi-orthogonal space-time block coding (QOSTBC), and orthogonal space–time block coding (OSTBC) methods. We also compared its performance to that of Hadamard spreading diversity. Alamouti coding performs better than the proposed technique at the second order of transmit diversity, but is also limited to that order. The proposed technique performs better than OSTBC at the same order of the transmit diversity. QOSTBC performs slightly better than the proposed technique at the same order of transmit diversity. However, when all methods have the same detection complexity, the proposed technique performs better than both QOSTBC and Hadamard spreading diversity.     

测角目标定位的协方差矩阵旋转变换滤波算法

基于滤波量比预测量和测量量都准确这一原理,该文提出一种适用于只测角无源定位的非线性滤波算法——协方差矩阵旋转变换的推广Kalman滤波算法.文中推导了协方差矩阵变换的原理,给出了二维只测角无源定位应用的协方差矩阵旋转变换公式.仿真表明该算法比同类型的基于微分线性化和泛线性化的Kalman滤波算法具有更好的性能.     

基于圆形窗和HNCC的针对旋转图像的匹配方法

在基于区域的匹配方法中,匹配窗口一般是方形或长方形,如果存在变形,如旋转等,匹配将变得十分困难。提出了一种基于圆形窗和HNCC的匹配方法,首先把实时图分成几个方形窗口,以方形窗的内切圆作为匹配窗口,利用提出的HNCC方法在参考图中找出这些小窗口对应的控制点,并进行一致性检查去除误匹配点。根据坐标的转换模型和最小二乘方法,求出参考图与实时图的对应坐标关系。与现有的基于特征的匹配方法相比,此方法很容易得到控制点而不需要图像中有明显的特征,同时此方法简单、有效、容易理解。仿真试验证明了此方法的有效性。     

旋转人脸的模板匹配定位与旋转角度估算方法

本文实现了一种依靠非旋转的人脸模板对平面内旋转的人脸图象进行匹配定位与角度估算的方法。相对于通过由不同旋转角度的模板构成的集合中的成员分别作用于目标图象进行匹配定位的方法，本文的方法减轻了计算负担。而且本文将圆投影法与Zernike矩法相结合实现了旋转人脸图象的定位与旋转角度估算。其匹配的准确性比较高，而且具有良好的抗噪声特性。     

基于FRFT与WVD的旋转LFM信号参数估计

为了克服传统的全域搜索法在旋转LFM信号参数估计过程的繁琐问题,提出基于分数阶傅里叶变换(FRFT)与魏格纳分布(WVD)的旋转LFM信号参数估计方法.通过分析旋转LFM信号的性质和特性,给出了该信号的FRFT形式.基于WVD良好的时频分辨率,得到了清晰的调频信号时频分布,并且给出旋转LFM信号参数估计的具体步骤.仿真实验结果表明,该方法有效可行.     

Entropy-Controlled Artificial Anisotropic Diffusion for the Numerical Solution of Conservation Laws Based on Algorithms from Image Processing

In image processing are nonlinear anisotropic diffusion filters used to construct suitable filter algorithms for denoising, edge enhancement, and edge detection. We applied a nonlinear anisotropic diffusion operator in the context of the numerical solution of a scalar hyperbolic conservation law. It turns out that algorithms currently used in image processing are very well suited for the design of nonlinear higher-order dissipative terms. In particular we stabilize a central scheme, known for its oscillatory behavior, by the construction of a nonlinear diffusion term. This means constructing a diffusion matrix consisting of eigenvectors parallel and perpendicular to discontinuities and eigenvalues denoting the amount of dissipation depending on the local strength of the gradients. These directions are used to steer the amount of dissipation, which means suppressing diffusion across the shock front and using the perpendicular direction to enable the necessary diffusion to stabilize the underlying second-order scheme. This new approach allows a multidimensional view to the concept of artificial dissipation. We take the concept of entropy production in the vicinity of shock regions as an indicator for the steering of the diffusion matrix. In smooth regions, which obey an entropy equality instead of an entropy inequality, no information about the diffusion direction and strength is needed. So we add as a stabilizing term diffusion parallel to the characteristics, which turns out to be the Lax–Wendroff diffusion rate. In the case of unsteady regions we use the entropy production to blend between this diffusion term and an—still second-order—extra diffusion term with diffusion parallel to the gradient of the entropy production.     

基于旋转因子的差分酉空时分组码

基于TBH和Jafarkhan编码方案的两组准正交空时分组码,引入自适应旋转因子构造出四种差分调制酉矩阵,该方法不仅没有带来星座扩展,还使新的码字具有较大的欧氏距离。同时在接收端基于角度算子,形成了简化的成对译码方法。仿真结果表明：尽管此设计方法增加了一定的复杂度,但它比没有加入旋转因子的差分酉空时分组码具有更好的误码性能。     

双旋Y切石英振子厚度模式的频温特性的研究

本文利用描述固体中弹性声波的克里斯托费尔方程,建立了双旋Y切石英振子厚度模式的频温特性分析方法,并编制了相应的计算机程序。该程序可给出双旋Y切石英振子在任意切角(ф_3ф_1)下的厚度模(a、b、c模)的频率温度特性曲线。文中给出了单旋AT切、BT切(b模)、双旋SC切(b、c模)、FC切、IT切、LC切、NL_1切、NL_2切、AK切等各已知切型的频温特性曲线。对石英谐振器的切角灵敏度和切角误差进行了分析。