Multiple Multidimensional Morse Wavelets

This paper defines a set of operators that localize a radial image in space and radial frequency simultaneously. The eigenfunctions of the operator are determined and a nonseparable orthogonal set of radial wavelet functions are found. The eigenfunctions are optimally concentrated over a given region of radial space and scale space, defined via a triplet of parameters. Analytic forms for the energy concentration of the functions over the region are given. The radial function localization operator can be generalised to an operator localizing any L²(Ropf²) function. It is demonstrated that the latter operator, given an appropriate choice of localization region, approximately has the same radial eigenfunctions as the radial operator. Based on a given radial wavelet function a quaternionic wavelet is defined that can extract the local orientation of discontinuous signals as well as amplitude, orientation and phase structure of locally oscillatory signals. The full set of quaternionic wavelet functions are component by component orthogonal; their statistical properties are tractable, and forms for the variability of the estimators of the local phase and orientation are given, as well as the local energy of the image. By averaging estimators across wavelets, a substantial reduction in the variance is achieved     

Dyadic Green's function for a multilayered planar medium-a dyadic eigenfunction approach

A new formulation of the dyadic Green's function for a planarly layered medium is presented, based on dyadic eigenfunctions of the Green's function operator. The general development of the dyadic Green's function is shown, resulting in a three-dimensional purely spectral representation. The spectral form is converted to a Hankel-function form using standard techniques, analogous to the sum-of-residues plus branch-cut representation often obtained from the Sommerfeld Green's function. Advantages and disadvantages of both the eigenfunction and Hankel function forms are outlined, and compared to other Green's function representations. Examples of the Green's dyadic for free space and for a grounded dielectric slab environment are provided, and the role of the continuous and discrete spectrum is discussed.     

Integral transforms covariant to unitary operators and theirimplications for joint signal representations

Fundamental to the theory of joint signal representations is the idea of associating a variable, such as time or frequency, with an operator, a concept borrowed from quantum mechanics. Each variable can be associated with a Hermitian operator, or equivalently and consistently, as we show, with a parameterized unitary operator. It is well known that the eigenfunctions of the unitary operator define a signal representation which is invariant to the effect of the unitary operator on the signal, and is hence useful when such changes in the signal are to be ignored. However, for detection or estimation of such changes, a signal representation covariant to them is needed. Using well-known results in functional analysis, we show that there always exists a translationally covariant representation; that is, an application of the operator produces a corresponding translation in the representation. This is a generalization of a recent result in which a transform covariant to dilations is presented. Using Stone's theorem, the “covariant” transform naturally leads to the definition of another, unique, dual parameterized unitary operator. This notion of duality, which we make precise, has important implications for joint distributions of arbitrary variables and their interpretation. In particular, joint distributions of dual variables are structurally equivalent to Cohen's class of time-frequency representations, and our development shows that, for two variables, the Hermitian and unitary operator correspondences can be used consistently and interchangeably if and only if the variables are dual     

基于量子Haar小波的图像压缩

针对量子计算的Haar小波算法的研究现状,提出其在图像压缩方面的应用。引入正移置换矩阵,将经典Haar小波被分解为幺正矩阵直和、直积和点积的形式。再基于扩展Kronecker积将Haar小波矩阵表示为一系列的W-H矩阵和正移置换矩阵的组合。由此得出量子Haar小波的逻辑线路。最后创新性地采用量子模拟器进行量子Haar小波的彩色图像压缩实验,并给出实验结果。结果验证了量子Haar小波在图像压缩方面有着很好的可行性。     

分数Fourier变换、矩阵群和时-频分析

本文从矩阵群的观点出发讨论了分数Fourier变换的数学描述并通过数字仿真直观地说明了它进行信号时-频分析的两个特点.结果表明,在矩阵描述下,经典的Fourier变换相当于一个置换矩阵;一般的分数Fourier变换相当于一个广义置换矩阵;分数Fourier变换全体构成的变换族可以用一个矩阵群来描述,多次变换运算完全转化为相应的矩阵乘法运算.最后,数字信号分数Fourier变换的仿真计算表明,分数Fourier变换具有独特的时-频分析性质.     

General Analysis of a Parallel-Plate Waveguide Inhomogeneously Filled with Gyromagnetic Media

The boundary value problem for a parallel-plate waveguide filled with inhomogeneous gyromagnetic medium is expressed and thoroughly examined in terms of a linear operator equation. A suitable vector definition of transverse mode functions is given and their completeness and orthogonality are proved. Applying a new set of continuity conditions for field components normal to the cross-sectional interface, the transfer matrix for the multilayered parallel-plate waveguiding structure is determined and used to formulate a characteristic equation. The analysis is illustrated by the numerical investigation of eigenfunctions and eigenvalues of a two layer ferrite-air guide.     

Dyadic eigenfunctions and natural modes for hybrid waves in planar media

A new formulation for studying electromagnetic wave propagation in an open, planarly layered medium is presented based on eigenfunctions of the Hertzian potential dyadic Green's function operator. Due to the complicated coupling of scalar components of potential at material interfaces, elevation of the usual vector eigenfunction problem to dyadic level is found to lead to a convenient, compact representation of wave propagation phenomena. Although we study the source-free problem here, the three columns of the eigenfunction dyadics represent (up to an excitation-dependent amplitude) the vector fields excited by a given three-dimensional source. The general theory of dyadic eigenfunctions is presented, including orthogonality and the possibility of associated functions (root functions) at modal degeneracies, and an example of propagation in a grounded dielectric slab environment is provided.     

Spectral representation of self-adjoint problems for layeredanisotropic waveguides

Layered waveguides with lossless anisotropic layers in the polar configuration are analyzed through the unifying concept of a real self-adjoint operator. For a suitable definition of two-vector transverse eigenfunctions, general properties such as orthogonality and completeness relations are derived. The linear operator formalism is applied to closed waveguides inhomogeneously filled with anisotropic materials, including crystals and gyrotropic media. As an extension of the former theory to open waveguides, a grounded uniaxial dielectric slab with a coplanar optic axis is also analyzed: as for open isotropic waveguides, a complete spectral representation including the surface (proper eigenfunctions) and the pseudosurface modes (improper eigenfunctions) is presented     

Volumetric transformation of brain anatomy

Presents diffeomorphic transformations of three-dimensional (3-D) anatomical image data of the macaque occipital lobe and whole brain cryosection imagery and of deep brain structures in human brains as imaged via magnetic resonance imagery. These transformations are generated in a hierarchical manner, accommodating both global and local anatomical detail. The initial low-dimensional registration is accomplished by constraining the transformation to be in a low-dimensional basis. The basis is defined by the Green's function of the elasticity operator placed at predefined locations in the anatomy and the eigenfunctions of the elasticity operator. The high-dimensional large deformations are vector fields generated via the mismatch between the template and target-image volumes constrained to be the solution of a Navier-Stokes fluid model. As part of this procedure, the Jacobian of the transformation is tracked, insuring the generation of diffeomorphisms. It is shown that transformations constrained by quadratic regularization methods such as the Laplacian, biharmonic, and linear elasticity models, do not ensure that the transformation maintains topology and, therefore, must only be used for coarse global registration     

异构计算系统中基于遗传算法的任务分配与调度

任务分配与调度是异构计算系统(HCS)的核心问题之一。本文提出了一种对异构计算系统进行任务分配与调度的遗传算法。首先对HCS任务分配调度问题做出定义，然后分别讨论了问题的编码表示，种群初始化，染色体适应度函数设计。杂交、内部杂交与迁移遗传算子设计，控制参数自适应，算法的总体框架等。最后给出算法的仿真实验情况及实验结果分析与结论等。     

An automatic sequential recognition method for cortical auditory evoked potentials

The detection of cortical auditory evoked potentials (CAEP), which are part of the electroencephalogram (EEG) in reaction to acoustic stimuli, has important applications such as determining objective audiograms. The detection is usually performed by a human operator, with support from often basic signal processing methods. This paper presents a novel mechanism for the detection of CAEPs, which is fully automatic and stops the measurement when a given confidence is reached. This proposed detector comprises of three stages. First, a feature extraction by a wavelet transform parameterizes the time domain EEG signal by only few transform coefficients. This feature vector is then classified by a neural network which yields a binary vote on every EEG segment. Finally, a sequential statistical test is performed on successive classifications; this stops the measurement if a specified decision confidence has been reached. The adjustment of the detector according to a clinical database is discussed. Thus adjusted, the proposed CAEP detection scheme is applied to a study, and compared with a human operator. The results demonstrate that this method can attain similar results, but outperforms the human expert for stimulation levels close to the hearing threshold.     

分组排列模式下图像加密算法的扩散性能分析与实现

该文研究了分组排列模式下图像加密的扩散性能,提出了最优扩散性与无碰撞排列两个概念。最优扩散性指以最少的加密轮数实现图像的全局扩散性。在分组排列模式下,当且仅当排列算法满足无碰撞要求时,图像加密算法具备最优扩散性。根据无碰撞排列的概念提出了四叉树排列算法,并证明该算法可满足最优扩散性的要求。     

满足扩散准则的元素之集的性质

设f(x)是V_n上的布尔函数,本文研究了f(x)的满足扩散准则的元素集合R^c_f的性质.证明了,若degf(x)=n,则R^c_f为空集.对于所有的二次布尔函数而言,均有R^c_f中的元素个数大于等于2^n-1.还对一类函数的雪崩性质进行了讨论.给出布尔函数不含有非零线性结构的充分必要条件是ζ_f中含有n个线性无关的元素,其中ζ_f={(α_i|〈ζ,l_i〉≠0,0≤i≤2ⁿ-1},l_i为线性函数φ_αi=〈x,α_i〉的序列.还给出了一种2阶扩散准则布尔函数的构造.     

The radiation operator

The concept of the radiation operator is introduced to assist in the analysis of various problems involving sources and their radiation fields. It gives the field outside the source region as operating on the field of a point source. Because there is a simple connection between the radiation vector describing the far-field and the radiation operator, it can be used to define fields anywhere outside the source region from their values in the far-field zone. Another important properly of the radiation operator is its ability to express sources of fields given their radiation pattern and polarization in the far zone. The source of such a field can be written in the form of radiation operator operating on a current element, the delta function source. To interpret this in terms of computable functions, existing tables of operational rules for different classes of operators can be applied. Examples of radiation operators corresponding to different sources are given together with examples of sources corresponding to given radiation field patterns. Finally it is shown that the radiation operator allows a considerable simplification to the derivation of the multipole expansion theory when compared to the classical recursion-formula derivation through spherical harmonic eigenfunctions     

Genetic algorithms for finite mixture model based voxel classification in neuroimaging

Finite mixture models (FMMs) are an indispensable tool for unsupervised classification in brain imaging. Fitting an FMM to the data leads to a complex optimization problem. This optimization problem is difficult to solve by standard local optimization methods, such as the expectation-maximization (EM) algorithm, if a principled initialization is not available. In this paper, we propose a new global optimization algorithm for the FMM parameter estimation problem, which is based on real coded genetic algorithms. Our specific contributions are two-fold: 1) we propose to use blended crossover in order to reduce the premature convergence problem to its minimum and 2) we introduce a completely new permutation operator specifically meant for the FMM parameter estimation. In addition to improving the optimization results, the permutation operator allows for imposing biologically meaningful constraints to the FMM parameter values. We also introduce a hybrid of the genetic algorithm and the EM algorithm for efficient solution of multidimensional FMM fitting problems. We compare our algorithm to the self-annealing EM-algorithm and a standard real coded genetic algorithm with the voxel classification tasks within the brain imaging. The algorithms are tested on synthetic data as well as real three-dimensional image data from human magnetic resonance imaging, positron emission tomography, and mouse brain MRI. The tissue classification results by our method are shown to be consistently more reliable and accurate than with the competing parameter estimation methods.     

具有均匀差分分布的一类置换

本文研究了置换的差分分布，证明了如果一个置换的坐标函数的每个线性组合都有非零线性结构，则该置换具有均匀差分分布的充要条件，是它的坐标函数的每个非零线性组合都是只有一个恒变线性结构的部分ｂｅｎｔ函数，并且它的坐标函数的不同非零线性组合所具有的非零线性结构互不相同。还证明了如果一个偶数维置换的坐标函数的每个线性组合都有非零线性结构，则该置换一定不具有均匀差分分布。本文还研究了Ｋ．Ｎｙｂｅｒｇ构造的能够达到最大非线性度的置换，证明了这些置换都具有均匀差分分布，从而解决了具有均匀差分分布的置换的存在性问题。     

Calculation of the states of shallow donors in quantum wells in a magnetic field using plane wave expansion

A nonvariational method for calculating the states of shallow donors in quantum wells in a magnetic field is suggested. The method can be used in a wide range of magnetic fields, starting with zero. The method is based on the expansion of the electron-wave function in a basis of eigenfunctions of the Hamiltonian operator that describes a rectangular quantum well. The results obtained by this method are compared to the experimental data and to the results of calculations using different theoretical methods. The comparison shows that our method describes the observed spectrum of the shallow-donor states in quantum wells in a magnetic field with a higher accuracy than the methods used in the study by Chen et al.     

Projection approximation subspace tracking

Subspace estimation plays an important role in a variety of modern signal processing applications. We present a new approach for tracking the signal subspace recursively. It is based on a novel interpretation of the signal subspace as the solution of a projection like unconstrained minimization problem. We show that recursive least squares techniques can be applied to solve this problem by making an appropriate projection approximation. The resulting algorithms have a computational complexity of O(nr) where n is the input vector dimension and r is the number of desired eigencomponents. Simulation results demonstrate that the tracking capability of these algorithms is similar to and in some cases more robust than the computationally expensive batch eigenvalue decomposition. Relations of the new algorithms to other subspace tracking methods and numerical issues are also discussed     

Distributed scheduling of CDMA networks with minimal information

An algorithm which produces conflict-free communication schedules in mobility multihop radio networks is presented. These schedules are produced in a completely distributed manner. The algorithm is based on a globally known permutation on the nodes of the network. As a result the only knowledge needed on the part of individual nodes is the number of nodes in the network. This permutation guarantees that conflict-free schedules can be produced in a distributed manner. Two extensions to the basic permutation are discussed. The first enables neighboring nodes to enhance their communication schedules in a fast, robust, distributed manner. The second extension allows the algorithm to operate in the presence of secondary conflicts     

Extrapolation of electromagnetic responses from conducting objectsin time and frequency domains

Utilizing early time response and low-frequency data, the complete electromagnetic response of dimensional conducting structure is generated. By mutually complementary data, simultaneous extrapolation in time and frequency domains are carried out. This is performed through the use of the associated Hermite polynomials. The interesting property of the Hermite polynomials is that they are the eigenfunctions of the Fourier transform operator. This implies that if the time-domain response at a point in space from a three-dimensional conducting object is modeled by an associated Hermite series expansion, the frequency-domain response at the same point can be expressed as a scaled version of the same time-domain representation. Therefore using early time and low-frequency-domain response data, it is possible to reproduce the missing response in both of the domains. Examples are presented to illustrate the application of this methodology