Recursive filtering for two-dimensional random fields (Corresp.)

A class of recursive filtering problems for random fields with a two-dimensional parameter is considered. After a brief introduction of two-parameter stochastic calculus, a class of Markovian random fields generated by stochastic integral equations is defined and considered. It is then shown that the problem of estimating such a Markovian field in additive white Gaussian noise can be reduced to a recursive formalism. If the random field is itself Gaussian, the recursive formalism reduces to a finite set of stochastic integral equations involving the conditional mean and covariance.     

Space transformation methods in the representation of geophysicalrandom fields

Various aspects of multidimensional random fields are studied by means of space transformations. The latter are elegant and comprehensive Radon operations which can solve complex multidimensional problems by transforming them to a suitable unidimensional setting, where analysis is considerably simpler. It is shown that spatial correlation functions in Rⁿ are uniquely determined by means of their space transformations in R¹. Necessary and sufficient conditions are established in order that a spatial random field (in Rⁿ) be represented as the linear combination of pairwise uncorrelated random processes (in R¹). Space transformations provide analytically tractable criteria for testing the permissibility of correlation functions and constitute an attractive instrument for spatial and spatiotemporal random field simulation and for studying stochastic partial differential equations. Several examples and a case study are discussed     

Simplifications in the stochastic Fourier transform approach to random surface scattering

Further developments in the application of the stochastic Fourier transform approach (SFTA) to random surface scattering are presented. It is first shown that the infinite dimensional integral equation for the stochastic Fourier transform of the surface current can be reduced to the three dimensions associated with the random surface height and slopes. A three-dimensional integral equation of the second kind is developed for the average scattered field in stochastic Fourier transform space using conditional probability density functions. Various techniques for determining the transformed current (and, subsequently, the incoherent scattered power) from the average scattered field in stochastic Fourier transform space are developed and studied from the point of view of computational suitability. The case of vanishingly small surface correlation length is reexamined and the SFTA is found to provide erroneous results for the average scattered field due to the basic failure of the magnetic field integral equation (MFIE) in this limit.     

平稳信号的非均匀采样与仿真

文中引入平稳随机过程点的知识,建立了广义平稳随机信号的非均匀采样序列模型,推导了其数字频谱的一般公式,揭示出了传统的谱分析没有考虑采样时间间隔的非均匀性对信号的统计特性的影响,误把采样所得随机强度序列的功率谱当作平稳随机过程非均匀采样信号的功率谱。丈中分析了几种具有典型分布函数的随机采样情况,证明了均匀采样信号的数字频谱只是非均匀采样数字频谱的一种特例。     

Restriction of a Markov random field on a graph and multiresolutionstatistical image modeling

The association of statistical models and multiresolution data analysis in a consistent and tractable mathematical framework remains an intricate theoretical and practical issue. Several consistent approaches have been proposed previously to combine Markov random field (MRF) models and multiresolution algorithms in image analysis: renormalization group, subsampling of stochastic processes, MRFs defined on trees or pyramids, etc. For the simulation or a practical use of these models in statistical estimation, an important issue is the preservation of the local Markovian property of the representation at the different resolution levels. It is shown that this key problem may be studied by considering the restriction of a Markov random field (defined on some simple finite nondirected graph) to a part of its original site set. Several general properties of the restricted field are derived. The general form of the distribution of the restriction is given. “Locality” of the field is studied by exhibiting a neighborhood structure with respect to which the restricted field is an MRF. Sufficient conditions for the new neighborhood structure to be “minimal” are derived. Several consequences of these general results related to various “multiresolution” MRF-based modeling approaches in image analysis are presented     

Asymptotic Mean Stationarity of Sources With Finite Evolution Dimension

The notion of the evolution of a discrete random source with finite alphabet is introduced and its behavior under the action of an associated linear evolution operator is studied. Viewing these sources as possibly stable dynamical systems it is proved that all random sources with finite evolution dimension are asymptotically mean stationary, which implies that such random sources have ergodic properties and a well-defined entropy rate. It is shown that the class of random sources with finite evolution dimension properly generalizes the well-studied class of finitary stochastic processes, which includes (hidden) Markov sources as special cases.     

The statistical analysis of space-time point processes

A space-time point process is a stochastic process having as realizations points with random coordinates in both space and time. We define a general class of space-time point processes which we term {em analytic}. These are point processes that have only finite numbers of points in finite time intervals, absolutely continuous joint-occurrence distributions, and for which points do not occur with certainty in finite time intervals. Analytic point processes possess an intensity determined by the past of the point process. As a class, analytic point processes remain closed under randomization by a parameter. The problem we consider is that of estimating a random parameter of an observed space-time point process. This parameter may be drawn from a function space and can, therefore, model a random variable, random process, or random field that influences the space-time point process. Feedback interactions between the point process and the randomizing parameter are included. The conditional probability measure of the parameter given the observed space-time point process is a sufficient statistic for forming estimates satisfying a wide variety of performance criteria. A general representation for this conditional measure is developed, and applications to filtering, smoothing, prediction, and hypothesis testing are given.     

Wavelet decomposition of harmonizable random processes

The discrete wavelet decomposition of second-order harmonizable random processes is considered. The deterministic wavelet decomposition of a complex exponential function is examined, where its pointwise and bounded convergence to the function is proved. This result is then used for establishing the stochastic wavelet decomposition of harmonizable processes. The similarities and differences between the wavelet decompositions of general harmonizable processes and a subclass of processes having no spectral mass at zero frequency, e.g., those that are wide-sense stationary and have continuous power spectral densities, are also investigated. The relationships between the harmonization of a process and that of its wavelet decomposition are examined. Finally, certain linear operations such as addition, differentiation, and linear filtering on stochastic wavelet decompositions are considered. It is shown that certain linear operations can be performed term by term with the decomposition     

无线电波传播中的随机射线及其应用

对建模无线电波传播的随机射线进行了详细的阐述,从随机网格信道引出随机射线的概念,介绍了随机射线的产生背景和分类,并给出一种产生随机射线的数学模型随机桥过程。使用最大熵原理得到发生后次反射随机射线的概率分布。最后介绍使用随机射线建模超宽带室内信道的多径传播轨,在此基础上可以得到信道特性建模的基本随机变量,以及无线电波传播的概率模型等应用。     

平稳随机过程非均匀采样信号的数字谱研究

目前的随机信号分析多是基于作等时间间隔采样以描述信号特征,而实际应用中往往不能避免采样的非均匀性;传统的谱分析方法必然产生原理误差。本文引入平稳随机点过程的知识,建立了广义平稳随机信号的非均匀采样序列模型,推导了其数字频谱的一般公式,分析了具有典型分布函数的随机采样情况。     

Likelihood calculation for a class of multiscale stochastic models,with application to texture discrimination

A class of multiscale stochastic models based on scale-recursive dynamics on trees has previously been introduced. Theoretical and experimental results have shown that these models provide an extremely rich framework for representing both processes which are intrinsically multiscale, e.g., 1/f processes, as well as 1D Markov processes and 2D Markov random fields. Moreover, efficient optimal estimation algorithms have been developed for these models by exploiting their scale-recursive structure. The authors exploit this structure in order to develop a computationally efficient and parallelizable algorithm for likelihood calculation. They illustrate one possible application to texture discrimination and demonstrate that likelihood-based methods using the algorithm achieve performance comparable to that of Gaussian Markov random field based techniques, which in general are prohibitively complex computationally.     

A generalized SSI reliability model considering stochastic loading and strength aging degradation

A generalized stress-strength interference (SSI) reliability model to consider stochastic loading and strength aging degradation is presented in this paper. This model conforms to previous models for special cases, but also demonstrates the weakness of those models when multiple stochastic elements exist. It can be used for any nonhomogeneous Poisson loading process, and any kind of strength aging degradation model. To solve the SSI reliability equation, a numerical recurrence formula is presented based on the Gauss-Legendre quadrature formula to calculate multiple integrations of a random variable vector. Numerical analysis of three examples shows this SSI reliability model provides accurate results for both homogeneous & nonhomogeneous Poisson loading processes.     

Stochastic differential equations: an approach to the generation ofcontinuous non-Gaussian processes

The generation of continuous random processes with jointly specified probability density and covariation functions is considered. The proposed approach is based on the interpretation of the simulated process as a stationary output of a nonlinear dynamic system, excited by white Gaussian noise and described by a system of a first-order stochastic differential equations (SDE). The authors explore how the statistical characteristics of the equation's solution depends on the form of its operator and on the intensity of the input noise. Some aspects of the approximate synthesis of stochastic differential equations and examples of their application to the generation of non-Gaussian continuous processes are considered. The approach should be useful in signal processing when it is necessary to translate the available a priori information on the real random process into the language of its Markov model as well as in simulation of continuous correlated processes with the known probability density function     

矩阵随机过程在短程无线信道空时特性建模中的应用

使用矩阵随机过程对短程无线信道的空时特性进行研究。以随机矩阵的列向量描述信道的仰角自由度,行向量描述信道的水平角自由度。使用自由布朗桥过程产生的样本描述无线信道中的多径分量的传播轨迹,在一定的映射规则下可以得到反映无线信道空时特性冲激响应的传统模型和矩阵随机过程模型。对无线信道的空时特性进行了仿真分析,仿真结果表明,自由布朗桥过程所描述的完全随机的约束环境中,多径分量的波达方向在仰角和水平角维度上显示出一定的局部偏好性。     

Simulated annealing in compound Gaussian random fields [imageprocessing]

Recently, a stochastic relaxation technique called simulated annealing has been developed to search for a globally optimal solution in image estimation and restoration problems. The convergence of simulated annealing has been proved only for random fields with a compact range space. Because of this, images were modeled as random fields with bounded discrete or continuous values. However, in most image processing problems, it is more natural to model the image as a random field with values in a noncompact space, e.g. conditional Gaussian models. The proof of convergence of the stochastic relaxation method is extended to a class of compound Gauss-Markov random fields. Simulation results are provided to show the power of these methods     

Stochastic models for random-request availability

The system receives a stream of tasks which arrive according to some random processes. A new availability measure, random-request availability, is proposed. This stochastic model provides closed-form mathematical expressions which incorporate the 3 basic elements: random task arrivals; system state; and operational requirements of the system. An analytic model is derived and illustrated by numerical examples     

随机桥过程研究短程无线信道的空时特性

使用随机桥过程的样本建模短程无线信道中多径分量的传播轨迹。由随机桥过程的样本构造出基本随机变量,在一定的映射规则下由基本随机变量的样本得到反映无线信道空时特性的多径时延、多径信号抽头增益、多径信号的波达方向等参量。使用随机桥过程的特例布朗桥过程,分别对散射体均匀分布的信道传播环境和有约束的无线信道传播环境的空时特性进行仿真分析。仿真结果表明,在这两种传播环境中,多径分量的波达方向在仰角和水平角维度上均存在一定的局部偏好性,不满足均匀分布的假设。在仰角-水平角-多径分量到达时延这3个自由度的空间中,多径分量的分布表现出一定的规律性。     

Stereo matching using colour consistency and hierarchical stochastic diffusion

A stereo matching algorithm is proposed using colour consistency and hierarchical stochastic diffusion. The colour consistency is introduced to the prior Markov random field (MRF) model to consider both the smoothness and the discontinuity of the disparity field. The energy function derived from the MRF model is minimised in the hierarchical stochastic diffusion, which first propagates the probability distribution of the reliable disparity field into the neighbourhood. Experimental results show good disparity maps compared with other propagation based methods.     

有色噪声的扩散过程模型

研究使用基于随机微分方程的扩散过程模型产生有色噪声.首先给出Markov扩散过程的平稳分布,该分布给出了扩散过程模型中的漂移系数、扩散系数和有色噪声概率密度分布之间的关系;选择扩散过程模型中的扩散系数为x的一次幂,其系数决定了所生成噪声的相关特性;数值算法使用Milstein高阶法.以三元独立积构造的G-分布雷达杂波为例进行仿真分析,验证所提出方法的准确性和有效性.