Efficient generation of conditional simulations by chebyshev matrix polynomial approximations to the symmetric square root of the covariance matrix

Consider the problem of generating a realization y₁ of a Gaussian random field on a dense grid of points ₁ conditioned on field observations y₂ collected on a sparse grid of points ₂. An approach to this is to generate first an unconditional realization y over the grid =_{1 2}, and then to produce y₁ by conditioning y on the data y₂. As standard methods for generating y, such as the turning bands, spectral or Cholesky approaches can have various limitations, it has been proposed by M. W. Davis to generate realizations from a matrix polynomial approximations to the square root of the covariance matrix. In this paper we describe how to generate a direct approximation to the conditional realization y₁, on ₁ using a variant of Davis' approach based on approximation by Chebyshev polynomials. The resulting algorithm is simple to implement, numerically stable, and bounds on the approximation error are readily available. Furthermore we show that the conditional realization y₁ can be generated directly with a lower order polynomial than the unconditional realization y, and that further reductions can be achieved by exploiting a nugget effect if one is present. A pseudocode version of the algorithm is provided that can be implemented using the fast Fourier transform if the field is stationary and the grid ₁ is rectangular. Finally, numerical illustrations are given of the algorithm's performance in generating various 2-D realizations of conditional processes on large sampling grids.     

图像平滑算法比较研究及改进策略

图像平滑作为去除图像中含有噪声的图像增强处理技术，是各种与图像有关软件中必不可少的功能模块。文中在分析噪声模型的基础上，对均值平滑、中值平滑、边缘保持平滑等技术从图像处理空间域中的算法原理、实现方法及效率等方面进行了详细比较。针对图像中含有的不同噪声模型，通过多次试验，得出了值得从事图像处理研究者参考的结论。这将有助于提高图像处理软件开发的效率。     

2002年CT扫描和三维成像学术年会评述

由CT理论与应用研究编辑部和北京信息工程学院主办、有中国体视学学会多位理事和会员参加的“2002年CT扫描和三维成像研讨会（CT科技学术年会）”于2002年10月18－20日，在北京大学逸夫苑理科楼学术报告厅举行。中国体视学学会副理事长刘国权教授出席致辞，对于这次CT科技年会的召开表示祝贺，并介绍了2003年在美国圣迭戈和北京将要召开第11届国际体视学会大会的有关情况，希望有关专家准备论文出席，来自全国各地48位专家，教授出席了会议，本次会议涉及CT理论、计算方法和软件及硬件技术；医学CT扫描成像和疾病诊断；工业CT和三维成像：地球层析和工程CT。美国爱荷华大学王革教授，纽约罗彻斯特大学宁若拉教授专程到会，分别做了精彩的特邀主题报告：显微CT的锥束重建新方法和近年来在这方面的进展和展望”，“锥光束三维CT技术在美国的过去、现在和未来”“国内专家也报告了前沿研究的新成果，在会前，CT理论与应用研究编辑部，根据收到的论文和摘要汇编和印制了专集，在会议最后一天，召开了“CT理论与应用研究”期刊编委会，传达了中国科协对于办好科技期刊的新要求，会议开得很成功。     

Conditional curvilinear stochastic simulation using pixel-based algorithms

In geology, structures displaying differing local directions of continuity are widespread, a typical example being a flusial depositional system. Conventional pixel-based geostatistical algorithms, may fail to reproduce such curvilinear structures. Conversely, object-based algorithms can reproduce curvilinear shapes but are difficult to condition to dense local data. Local depositional directions as obtained from dipmeter data. 3D seismic data, and geological interpretation represent critical information. An improved pixel-based geostatistical algorithm is proposed to account for such directional information. Case studies demonstrate the potential and limitations of the algorithm.     

SEDIMENT TRANSPORT MODEL OF A WATERSHED

ChinaisoneOfthecountrieswhichsufferfromthemostserioussoilerosionintheworld,andthehillyandgullyareasof~PlateauinthemiddlereachesOftheYellowRiverarethemostseriouserosionareainChina.Inthisarea,themainerosivefactorsarerainfallandrunoff.Sometimes,thesedimentyieldinasinglefloodeventcanbe40%oftheannualsedimentload.Therefore,itisveryimPOrtanttostudytheyieldandgraphOfSedimentOfsinglefindevent.Forthispn~,thispaperiswritten.AInongsedimentmodelsforsinglefloodevent,moreandmoreattentionwaspaidtOunitse…     

Transformation of Residuals to Avoid Artifacts in Geostatistical Modelling with a Trend

Trend modelling is an important part of natural resource characterization. A common approach to account for a variable with a trend is to decompose it into a relatively smoothly varying trend and a more variable residual component. Then, the residuals are stochastically modelled independent of the trend. This decomposition can result in values outside the plausible range of variability, such as grades below zero or ratios that exceed 1.0. We transform the residuals conditional to the trend component to explicitly remove these complex features prior to geostatistical modelling. Back transformation of the modelled residual values allows the complex relations to be reproduced. A petroleum-related application shows the robustness of the proposed transformation. Furthermore, a mining application shows that when this conditional transformation is applied to the original variable, instead of the residual, simulated values are assured to be nonnegative.     

Histogram and variogram inference in the multigaussian model

Several iterative algorithms are proposed to improve the histogram and variogram inference in the framework of the multigaussian model. The starting point is the variogram obtained after a traditional normal score transform. The subsequent step consists in simulating many sets of gaussian values with this variogram at the data locations, so that the ranking of the original values is honored. The expected gaussian transformation and the expected variogram are computed by an averaging operation over the simulated datasets. The variogram model is then updated and the procedure is repeated until convergence. Such an iterative algorithm can adapt to the case of tied data and despike the histogram. Two additional issues are also examined, referred to the modeling of the empirical transformation function and to the optimal pair weighting when computing the sample variogram.     

Lame surfaces as a generalisation of the triaxial ellipsoid

In modern geodesy the triaxial ellipsoid as a generalisation of the ellipsoid of revolution has a significant position in studying the figure of the Earth. Lame surfaces represent a generalisation of the triaxial ellipsoid. The following paragraphs are devoted to curvatures of the Lame surfaces.     

Conditional Simulation of Random Fields with Bivariate Gamma Isofactorial Distributions

This work focuses on a random function model with gamma marginal and bivariate isofactorial distributions, which has been applied in mining geostatistics for estimating recoverable reserves by disjunctive kriging. The objective is to widen its use to conditional simulation and further its application to the modeling of continuous attributes in geosciences. First, the main properties of the bivariate gamma isofactorial distributions are analyzed, with emphasis in the destructuring of the extreme values, the presence of a proportional effect (higher variability in high-valued areas), and the asymmetry in the spatial correlation of the indicator variables with respect to the median threshold. Then, we provide examples of stationary random functions with such bivariate distributions, for which the shape parameter of the marginal distribution is half an integer. These are defined as the sum of squared independent Gaussian random fields. An iterative algorithm based on the Gibbs sampler is proposed to perform the simulation conditional to a set of existing data. Such ‘multivariate chi-square’ model generalizes the well-known multigaussian model and is more flexible, since it allows defining a shape parameter which controls the asymmetry of the marginal and bivariate distributions.