Scale-Space Properties of Nonstationary Iterative Regularization Methods

Most scale-space concepts have been expressed as parabolic or hyperbolic partial differential equations (PDEs). In this paper we extend our work on scale-space properties of elliptic PDEs arising from regularization methods: we study linear and nonlinear regularization methods that are applied iteratively and with different regularization parameters. For these so-called nonstationary iterative regularization techniques we clarify their relations to both isotropic diffusion filters with a scalar-valued diffusivity and anisotropic diffusion filters with a diffusion tensor. We establish scale-space properties for iterative regularization methods that are in complete accordance with those for diffusion filtering. In particular, we show that nonstationary iterative regularization satisfies a causality property in terms of a maximum–minimum principle, possesses a large class of Lyapunov functionals, and converges to a constant image as the regularization parameters tend to infinity. We also establish continuous dependence of the result with respect to the sequence of regularization parameters. Numerical experiments in two and three space dimensions are presented that illustrate the scale-space behavior of regularization methods.     

A unified view of parametric processing algorithms for prewindowed signals

This paper offers a unified overview of the algorithms developed for the processing of ‘prewindowed’ signals. The prewindowing assumption leads to simple and efficient schemes which find applications in many areas of modern DSP but especially in the digital communications field (adaptive equalization, echo cancellation, etc.). Algorithms for both least-squares filtering and linear prediction of multichannel signals are considered. The multichannel approach was chosen here instead of the single-channel one because in some situations the generalization of the single-channel case is not trivial. (The inverse is trivial.) On the other hand, an increasing number of researchers is willing to practice multichannel DSP (biological signals, beamforming techniques in radar applications, etc.) and can find in those algorithms a tool ‘ready for use’. The presentation covers fast order-recursive schemes and sequential methods for direct (transversal) and lattice-ladder implementations. In the latter case, normalized and unnormalized lattice-ladder forms are discussed. The derivation of all algorithms using a unified approach reveals the relationships among the various variables and between fast algorithms for direct and lattice-ladder structures.     

Maxwell 方程组的多辛算法

Maxwell方程在线性、各向同性、均匀、无源的介质中具有自然的多辛结构,可以表示为多辛Hamilton系统。Maxwell方程的多辛算法即对Maxwell方程在时间、空间同时进行保辛离散得到相应的差分格式。文中给出了5种麦克斯韦方程的多辛算法,分析并比较了这5种方法的数值色散特性。数值计算结果表明这些算法能很好地保持Maxwell方程的离散全局能量守恒特性。     

SPH的核近似和粒子近似

光滑粒子流体动力学(SPH,Smoothed Particle Hydrodynamic)方法是一种具有纯La-grangian性质的无网格方法,在众多学科和领域得到了广泛发展和重要应用。文中主要对用SPH方法近似偏微分方程(PDEs)的核近似法和粒子近似法进行了描述分析,并说明了两个的利弊。除了一些简单情况,PDEs的解析解是很难求出的,因此描述分析这两种方法对寻得近似解就具有十分重要的意义。     

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).     

The analysis of coupled interconnect with process parameter variation based wavelet collocation method

In this paper, a novel approach based on fast wavelet collocation method (FWCM) is presented to solve partial differential equations (PDEs) in coupled on-chip interconnects with parameter variations. After processing PDEs by decomposing variables with wavelet functions, we transfer the PDEs into ordinary differential equations (ODEs), and then use Taylor expansion in the ODEs to approximate the partial complex expression containing inverse matrix. Consequently, we can solve the PDEs with random variables more feasibly. Moreover, this approach provides a new idea for solving other kinds of PDEs with random variables in very large scaled integrated circuits (VLSI). Comparison with HSPICE simulation results shows the method proposed in this paper is effective and accurate.     

Reciprocity, discretization, and the numerical solution of directand inverse electromagnetic radiation and scattering problems

The author gives a formulation, based on Lorentz reciprocity, that unifies the finite element method (FEM) and the integral equation models. Wave propagation and scattering problems in electromagnetics have to be addressed with the aid of numerical techniques. Many of these methods can be envisaged as being discretized versions of appropriate weak formulations of the pertinent operator (differential or integral) equations. For the relevant problems as formulated in the time Laplace-transform domain it is shown that the Lorentz reciprocity theorem encompasses all known weak formulations, while its discretization leads to the discretized forms of the corresponding operator equations, in particular to their finite-element and integral-equation modeling schemes. Both direct (forward) and inverse problems are discussed     

A Moving Average Non-Homogeneous Poisson Process Reliability Growth Model to Account for Software with Repair and System Structures

We develop a moving average non-homogeneous Poisson process (MA NHPP) reliability model which includes the benefits of both time domain, and structure based approaches. This method overcomes the deficiency of existing NHPP techniques that fall short of addressing repair, and internal system structures simultaneously. Our solution adopts a MA approach to cover both methods, and is expected to improve reliability prediction. This paradigm allows software components to vary in nature, and can account for system structures due to its ability to integrate individual component reliabilities on an execution path. Component-level modeling supports sensitivity analysis to guide future upgrades, and updates. Moreover, the integration capability is a benefit for incremental software development, meaning only the affected portion needs to be re-evaluated instead of the entire package, facilitating software evolution to a higher extent than with other methods. Several experiments on different system scenarios and circumstances are discussed, indicating the usefulness of our approach.     

Automated topology synthesis of analog and RF integrated circuits: A survey

The puzzle of automatically synthesizing analog and radio frequency (RF) circuit topology has not yet been offered with an industrially-acceptable solution although endeavors still continue to seek a conquest in this area. This survey provides a comprehensive study of the techniques utilized for this purpose. The existing methods are analyzed from four different viewpoints, namely, structural view, conceptual view, implementation view, and application view. Different schemes are perused with their advantages and drawbacks discussed in the context of balanced performance between configuration-space coverage and search efficiency. Some prospective trends are pointed out to shed light on the upcoming research activities.     

素数域上椭圆曲线密码体制的软件实现

椭圆曲线密码体制已成为公钥密码研究的主流。介绍了椭圆曲线密码体制的一些数学理论基础,对算法的基础模块进行了说明,讨论了软件实现素数域上椭圆曲线密码算法的一种方法,在DSP6205,主频200MHz的环境下,192比特的ECDSA签名速率70次/秒,验证速率60次/秒。最后对椭圆曲线加密体制的研究与实现进行了全面总结,给出了所完成的工作,对椭圆曲线密码体制的应用前景提出了展望。     

A massively parallel computation strategy for FDTD: time and spaceparallelism applied to electromagnetics problems

We present a novel strategy for incorporating massive parallelism into the solution of Maxwell's equations using finite-difference time-domain methods. In a departure from previous techniques wherein spatial parallelism is used, our approach exploits massive temporal parallelism by computing all of the time steps in parallel. Furthermore, in contrast to other methods which appear to concentrate on explicit schemes such as Yee's (1966) algorithm, our strategy uses the implicit Crank-Nicolson technique which provides superior numerical properties. We show that the use of temporal parallelism results in algorithms which offer a massive degree of coarse grain parallelism with minimum communication and synchronization requirements. Due to these features, the time-parallel algorithms are particularly suitable for implementation on emerging massively parallel multiple instruction-multiple data (MIMD) architectures. The methodology is applied to a circular cylindrical configuration, which serves as a testbed problem for the approach, to demonstrate the massive parallelism that can be exploited. We also discuss the generalization of the methodology for more complex problems     

Modeling Electron Transport in Vertical-SOI NMOSFET by Directly Solving BTE with FEA

A numerical schemes applicable to the direct solution of Boltzmann transport equation (BTE) in vertical-SOI NMOSFET are investigated by means of the finite element analysis (FEA). The solution gives the electron distribution function, electrostatic potential, carriers concentration, drift velocity, average energy and drain current by directly solving the BTE and the Poisson equation self-consistency. The result shows that the direct numerical solution of the BTE with the aid of FEA and vertical SOI NMOSFET is a promising approach for ultra short channel transistors modeling.     

On the theory of the synthesis of offset dual-shapedreflectors-case examples

In an earlier paper by V. Galindo-Israel et al. (see ibid., vol.AP-35, p.887-96, August 1987) the geometrical optics (GO) principles, constraints, and requirements of the dual- and single-offset-shaped reflector synthesis problem were collected and developed into a set of nonlinear first-order partial differential equations (PDEs). Methods of solving these PDEs numerically were illustrated, as were certain problems that may arise. An extension of the methods by which solutions to the PDEs can be obtained is presented, together with several case examples. These examples are independently analyzed by GO and physical optics diffraction methods. The starting point for the integration over each reflector can be taken on the outer rim, at the center, or at an intermediate point-the intermediate starting point being the more general case. The utility of the speed of this synthesis method is demonstrated. This makes practical the incorporation of the synthesis into a search algorithm that can optimize one or more parameters of the reflector system. As an example, the optimization of the mapping equations for low cross polarization is discussed     

Two-dimensional simulation for resonant tunneling transistor

A new two-dimensional device simulation for the resonant tunneling transistor is presented. In the simulation, the one-dimensional Schrodinger equation is solved for the intrinsic area of the transistor and the conventional two-dimensional drift-diffusion equations are solved for the extrinsic part. Both equations are coupled with the carrier generation-recombination term in the drift-diffusion equations. In addition, the Poisson equation is also solved self-consistently with them to take the charge distribution effect into account. The two-dimensional simulator has been successfully applied to the analysis of a resonant tunneling transistor and it was found that the current-voltage characteristics sensitively depend on the base resistance. This means that a two-dimensional treatment of the voltage drop in the base region is essential for an accurate simulation     

MRTD: new time-domain schemes based on multiresolution analysis

The application of multiresolution analysis to Maxwell's equations results in new multiresolution time-domain (MRTD) schemes with unparalleled inherent properties. In particular, the approach allows the development of MRTD schemes which are based on scaling functions only or on a combination of scaling functions and wavelets leading to a variable mesh grading. The dispersion of the MRTD schemes compared to the conventional Yee finite-difference time-domain (FDTD) scheme shows an excellent capability to approximate the exact solution with negligible error for sampling rates approaching the Nyquist limit. Simple microwave structures including dielectric materials are analyzed in order to illustrate the application of the MRTD schemes and to demonstrate the advantages over Yee's FDTD scheme with respect to memory requirements and execution time     

Comparative analysis of torque-controlled IM drives withapplications in electric and hybrid vehicles

This paper presents torque-controlled drives based on machine flux and torque estimation. The theoretical aspects of these methods are discussed and a comparative analysis is provided with emphasis on DSP implementation and experimental results. The problems in the application of these techniques to propulsion systems are also discussed and possible solutions are presented     

Difference methods for the solution of the time-dependent semiconductor flow equations

The letter describes the solution of the instationary semiconductor transport equations by means of finite-difference methods. This new approach is based on the formal similarity with the equations of incompressible flow. Implicit schemes have proven useful for the computation of both transient and steady-state solutions. Comparisons with experimental results are extremely favourable for f.e.t.s.     

An Iterative Approach to the Finite-Element Method in Field Problems

An iterative approach to the finite-element method is presented. Several finite-element formulations are presented for the Laplace, Poisson, and Helmholtz equations. These formulations permit iterative solutions. The convergence of the vector sequences generated by the iterative method is accelerated using successive extrapolation and other methods. Accuracy and convergence of the solutions are discussed.