SChoA: a newly fusion of sine and cosine with chimp optimization algorithm for HLS of datapaths in digital filters and engineering applications

The spectral Legendre–Galerkin method for solving a two-dimensional nonlinear system of advection–diffusion–reaction equations on a rectangular domain is presented and compared with analytical solution. The proposed method is based on the Legendre–Galerkin formulation for the linear terms and computation of the nonlinear terms in the Chebyshev–Gauss–Lobatto points. The main difference of the spectral Legendre–Galerkin method presented in the current paper with the classic Legendre–Galerkin method is in treating the nonlinear terms and imposing boundary conditions. Indeed, in the spectral Legendre–Galerkin method the nonlinear terms are efficiently handled using the Chebyshev–Gauss–Lobatto points and also the boundary conditions are imposed strongly as collocation methods. Combination of the proposed method with a semi-implicit time integration method such as the Leapfrog–Crank–Nicolson scheme leads to reducing the complexity of computations and obtaining a linear algebraic system of equations. Efficiency and spectral accuracy of the proposed method are demonstrated numerically by some examples.

     

A Spectral Element Approximation to Price European Options with One Asset and Stochastic Volatility

We develop a Legendre quadrilateral spectral element approximation for the Black-Scholes equation to price European options with one underlying asset and stochastic volatility. A weak formulation of the equations imposes the boundary conditions naturally along the boundaries where the equation becomes singular, and in particular, we use an energy method to derive boundary conditions at outer boundaries for which the problem is well-posed on a finite domain. Using Heston’s analytical solution as a benchmark, we show that the spectral element approximation along with the proposed boundary conditions gives exponential convergence in the solution and the Greeks to the level of time and boundary errors in a domain of financial interest.     

A New Spectral Element Method for Pricing European Options Under the Black–Scholes and Merton Jump Diffusion Models

We present a new spectral element method for solving partial integro-differential equations for pricing European options under the Black?CScholes and Merton jump diffusion models. Our main contributions are: (i)?using an optimal set of orthogonal polynomial bases to yield banded linear systems and to achieve spectral accuracy; (ii)?using Laguerre functions for the approximations on the semi-infinite domain, to avoid the domain truncation; and (iii)?deriving a rigorous proof of stability for the time discretizations of European put options under both the Black?CScholes model and the Merton jump diffusion model. The new method is flexible for handling different boundary conditions and non-smooth initial conditions for various contingent claims. Numerical examples are presented to demonstrate the efficiency and accuracy of the new method.     

基于阈值的小波域语音增强新算法

提出了一种新的基于阈值的小波域语音增强算法,采用Bark尺度小波包对含噪语音进行分解,以模拟人耳的听觉特性.采用结点阈值法,用基于谱熵的方法估计结点噪声,实验表明,该算法在多种噪声,尤其是有色噪声和非平稳噪声条件下均有较好的语音增强效果.     

Domain Decomposition Spectral Method for Mixed Inhomogeneous Boundary Value Problems of High Order Differential Equations on Unbounded Domains

In this paper, we develop domain decomposition spectral method for mixed inhomogeneous boundary value problems of high order differential equations defined on unbounded domains. We introduce an orthogonal family of new generalized Laguerre functions, with the weight function x ^?? , ?? being any real number. The corresponding quasi-orthogonal approximation and Gauss-Radau type interpolation are investigated, which play important roles in the related spectral and collocation methods. As examples of applications, we propose the domain decomposition spectral methods for two fourth order problems, and the spectral method with essential imposition of boundary conditions. The spectral accuracy is proved. Numerical results demonstrate the effectiveness of suggested algorithms.     

基于实值离散Gabor变换的谱减法语音增强

提出了一个基于实值离散Gabor变换的新的谱减法语音增强,采用高斯窗作为综合窗,利用已有的快速实值离散Gabor变换将语音变换到时频域,噪声估计采用改进的最优滤波和最小统计的martin算法,在联合时频域进行谱减得到纯净语音增益,在得到语音增强信号后,利用实值离散Gabor逆变换将其还原输出。实验结果表明,在分段信噪比和语音质量方面均与目前主流谱减法相比均有提高。     

A new approach for thresholding spectral change detection using multispectral and hyperspectral image data,a case study over Sokolov,Czech republic

Change detection and multitemporal analyses aim to detect changes occurring over a specific geographical area using two or more images acquired at two or more different times. In this article, we present a new thresholding approach for unsupervised change detection. This approach focuses on determining the threshold that discriminates between change and no-change pixels. The differences between pixels in the two images are associated with real changes or noise. We propose a thresholding scheme that separates the threshold into two parts: (1) a spectral domain threshold that accounts for errors related to sensor stability, atmospheric conditions, and data-processing variations, and (2) a spatial domain threshold associated with georectification errors. We demonstrate our method using both multispectral Landsat images and airborne imaging spectroscopy HyMap images. The results show that the spectral domain threshold gives high detection capabilities with moderate false-alarm rate. Adding the spatial domain threshold to the spectral domain threshold reduces the false-alarm rates while maintaining good detection capabilities.     

一种改进的基于谱熵的语音端点检测技术

论文提出了基于时频谱减增强和谱熵的语音端点检测算法。算法对带噪语音在频域利用谱减法去除宽带加性噪声,在时域去除由谱减带来的残差噪声从而对语音进行了增强。对增强后的语音利用谱熵特征进行端点检测。实验结果表明,此算法快速有效,具有较强的抗噪能力,特别适合低信噪比的语音端点检测。     

Efficient Chebyshev–Petrov–Galerkin Method for Solving Second-Order Equations

A new efficient Chebyshev–Petrov–Galerkin (CPG) direct solver is presented for the second order elliptic problems in square domain where the Dirichlet and Neumann boundary conditions are considered. The CPG method is based on the orthogonality property of the kth-derivative of the Chebyshev polynomials. The algorithm differs from other spectral solvers by the high sparsity of the coefficient matrices: the stiffness and mass matrices are reduced to special banded matrices with two and four nonzero diagonals respectively. The efficiency and the spectral accuracy of CPG method have been validated.     

基于时频结合的背景噪声下语音增强方法

本文在研究基于改进谱减法的基础之上,提出了在频域利用谱减法去除宽带加性噪声,在时域利用短时过零率和短时能量组合而成的加权函数去除谱减法后产生的“音乐噪声”的方法．实验表明：这种时频结合的语音增强方法对背景噪声下的语音质量的增强效果明显。     

Modeling of first-order photobleaching kinetics using Krylov subspace spectral methods

We solve the first order 2-D reaction–diffusion equations which describe binding-diffusion kinetics using the photobleaching scanning profile of a confocal laser scanning microscope, approximated by a Gaussian laser profile. We show how to solve the first-order photobleaching kinetics partial differential equations (PDEs) using a time-stepping method known as a Krylov subspace spectral (KSS) method. KSS methods are explicit methods for solving time-dependent variable-coefficient partial differential equations. They approximate Fourier coefficients of the solution using Gaussian quadrature rules in the spectral domain. In this paper, we show how a KSS method can be used to obtain not only an approximate numerical solution, but also an approximate analytical solution when using initial conditions that come from pre-bleach steady states and also general initial conditions, to facilitate asymptotic analysis. Analytical and numerical results are presented. It is observed that although KSS methods are explicit, it is possible to use a time step that is far greater than what the CFL condition would indicate.     

Clustering of biological time series by cepstral coefficients based distances

Clustering of stationary time series has become an important tool in many scientific applications, like medicine, finance, etc. Time series clustering methods are based on the calculation of suitable similarity measures which identify the distance between two or more time series. These measures are either computed in the time domain or in the spectral domain. Since the computation of time domain measures is rather cumbersome we resort to spectral domain methods. A new measure of distance is proposed and it is based on the so-called cepstral coefficients which carry information about the log spectrum of a stationary time series. These coefficients are estimated by means of a semiparametric model which assumes that the log-likelihood ratio of two or more unknown spectral densities has a linear parametric form. After estimation, the estimated cepstral distance measure is given as an input to a clustering method to produce the disjoint groups of data. Simulated examples show that the method yields good results, even when the processes are not necessarily linear. These cepstral-based clustering algorithms are applied to biological time series. In particular, the proposed methodology effectively identifies distinct and biologically relevant classes of amino acid sequences with the same physicochemical properties, such as hydrophobicity.     

3D point of interest detection via spectral irregularity diffusion

This paper presents a method for detecting points of interest on 3D meshes. It comprises two major stages. In the first, we capture saliency in the spectral domain by detecting spectral irregularities of a mesh. Such saliency corresponds to the interesting portions of surface in the spatial domain. In the second stage, to transfer saliency information from the spectral domain to the spatial domain, we rely on spectral irregularity diffusion (SID) based on heat diffusion. SID captures not only the information about neighbourhoods of a given point in a multiscale manner, but also cues related to the global structure of a shape. It thus preserves information about both local and global saliency. We finally extract points of interest by looking for global and local maxima of the saliency map. We demonstrate the advantages of our proposed method using both visual and quantitative comparisons based on a publicly available benchmark.     

Pose analysis using spectral geometry

We propose a novel method to analyze a set of poses of 3D models that are represented with triangle meshes and unregistered. Different shapes of poses are transformed from the 3D spatial domain to a geometry spectrum domain that is defined by Laplace–Beltrami operator. During this space-spectrum transform, all near-isometric deformations, mesh triangulations and Euclidean transformations are filtered away. The different spatial poses from a 3D model are represented with near-isometric deformations; therefore, they have similar behaviors in the spectral domain. Semantic parts of that model are then determined based on the computed geometric properties of all the mapped vertices in the geometry spectrum domain. Semantic skeleton can be automatically built with joints detected as well. The Laplace–Beltrami operator is proved to be invariant to isometric deformations and Euclidean transformations such as translation and rotation. It also can be invariant to scaling with normalization. The discrete implementation also makes the Laplace–Beltrami operator straightforward to be applied on triangle meshes despite triangulations. Our method turns a rather difficult spatial problem into a spectral problem that is much easier to solve. The applications show that our 3D pose analysis method leads to a registration-free pose analysis and a high-level semantic part understanding of 3D shapes.     

Elimination of end effects in local mean decomposition using spectral coherence and applications for rotating machinery

Local mean decomposition (LMD) is widely used in signal processing and fault diagnosis of rotating machinery as an adaptive signal processing method. It is developed from the popular empirical mode decomposition (EMD). Both of them have an open problem of end effects, which influences the performance of the signal decomposition and distort the results. Using the cyclostationary property of a vibration signal generated by rotating machinery, a novel signal waveform extension method is proposed to solve this problem. The method mainly includes three steps: waveform segmentation, spectral coherence comparison, and waveform extension. Its main idea is to automatically search the inside segment having similar frequency spectrum to one end of the analyzed signal, and then use its successive segment to extend the waveform, so that the extended signal can maintain temporal continuity in time domain and spectral coherence in frequency domain. A simulated signal is used to illustrate the proposed extension method and the comparison with the popular mirror extension and neural-network-based extension methods demonstrates its better performance on waveform extension. After that, combining the proposed extension method with normal LMD, the improved LMD method is applied to three experimental vibration signals collected from different rotating machines. The results demonstrate that the proposed waveform extension method based on spectral coherence can well extend the vibration signal, accordingly, errors caused by end effects would not distort the signal as well as its decomposition results.     

基于CNN和农作物光谱纹理特征进行作物分布制图

以卷积神经网络（Convolutional Neural Network, CNN）为代表的深度学习技术,在农作物遥感分类制图领域具有广阔的应用前景。以多时相Landsat 8 多光谱遥感影像为数据源,搭建CNN模型对农作物进行光谱特征提取与分类,并与支撑向量机（SVM）常规分类方法进行对比。进一步引入影像纹理信息,利用CNN对农作物光谱和纹理特征进行提取,优化作物分布提取结果。实验表明：① 基于光谱特征的农作物分布提取,验证结果对比显示,CNN对应各类别精度、总体精度均优于SVM,其中二者总体精度分别为95.14%和91.77%;② 引入影像纹理信息后,基于光谱和纹理特征的CNN农作物分类总体精度提高至96.43%,Kappa系数0.952,且分类结果的空间分布更为合理,可有效区分花生、道路等精细地物,说明纹理特征可用于识别不同作物。基于光谱和纹理信息的CNN特征提取,可面向种植结构复杂区域实现农作物精准分类与分布制图。     

基于CNN和农作物光谱纹理特征进行作物分布制图

以卷积神经网络（Convolutional Neural Network, CNN）为代表的深度学习技术，在农作物遥感分类制图领域具有广阔的应用前景。以多时相Landsat 8 多光谱遥感影像为数据源，搭建CNN模型对农作物进行光谱特征提取与分类，并与支撑向量机（SVM）常规分类方法进行对比。进一步引入影像纹理信息，利用CNN对农作物光谱和纹理特征进行提取，优化作物分布提取结果。实验表明：① 基于光谱特征的农作物分布提取，验证结果对比显示，CNN对应各类别精度、总体精度均优于SVM，其中二者总体精度分别为95.14%和91.77%；② 引入影像纹理信息后，基于光谱和纹理特征的CNN农作物分类总体精度提高至96.43%，Kappa系数0.952，且分类结果的空间分布更为合理，可有效区分花生、道路等精细地物，说明纹理特征可用于识别不同作物。基于光谱和纹理信息的CNN特征提取，可面向种植结构复杂区域实现农作物精准分类与分布制图。     

Spectral registration of noisy sonar data for underwater 3D mapping

3D mapping is very challenging in the underwater domain, especially due to the lack of high resolution, low noise sensors. A new spectral registration method is presented that can determine the spatial 6 DOF transformation between pairs of very noisy 3D scans with only partial overlap. The approach is hence suited to cope with sonar as the predominant underwater sensor. The spectral registration method is based on Phase Only Matched Filtering (POMF) on non-trivially resampled spectra of the 3D data.     

A modified Chebyshev pseudospectral DD algorithm for the GBH equation

In this paper, a Chebyshev spectral collocation domain decomposition (DD) semi-discretization by using a grid mapping, derived by Kosloff and Tal-Ezer in space is applied to the numerical solution of the generalized Burger’s-Huxley (GBH) equation. To reduce roundoff error in computing derivatives we use the above mentioned grid mapping. In this work, we compose the Chebyshev spectral collocation domain decomposition and Kosloff and Tal-Ezer grid mapping, elaborately. Firstly, the theory of application of the Chebyshev spectral collocation method with grid mapping and DD on the GBH equation is presented. This method yields a system of ordinary differential algebraic equations (DAEs). Secondly, we use a fourth order Runge-Kutta formula for the numerical integration of the system of DAEs. Application of this modified method to the GBH equation show that this method (M-DD) is faster and more accurate than the standard Chebyshev spectral collocation DD (S-DD) method.