杜 奕, 张 挺, 卢德唐, 李道伦. 一种基于改进Markov模型的插值方法[J]. 计算机研究与发展, 2012, 49(3): 565-571.
 引用本文: 杜 奕, 张 挺, 卢德唐, 李道伦. 一种基于改进Markov模型的插值方法[J]. 计算机研究与发展, 2012, 49(3): 565-571.
Du Yi, Zhang Ting, Lu Detang, Li Daolun. An Interpolation Method Using an Improved Markov Model[J]. Journal of Computer Research and Development, 2012, 49(3): 565-571.
 Citation: Du Yi, Zhang Ting, Lu Detang, Li Daolun. An Interpolation Method Using an Improved Markov Model[J]. Journal of Computer Research and Development, 2012, 49(3): 565-571.

## An Interpolation Method Using an Improved Markov Model

• 摘要: 重建过程中常常需要使用多种插值方法来提高重建精度,并结合多来源的数据进行整合.不同尺度、不同分辨率或不同类型的数据结合可以提高空间插值结果的精度.协同序贯高斯模拟(COSGSIM)能够利用已知的主要信息(硬数据)和一些模糊的辅助信息(软数据)来预测重建.协同区域化线性模型(LMC)和最初的Markov模型(简称MM1)被COSGSIM用于融合主要信息和辅助信息.但是LMC不能解决不同变量间交叉矩阵不稳定的问题.而MM1模型只有当主要信息定义在比较大的空间尺度时,才可以实现对COSGSIM的逼近.对于上述情况,提出一种改进的Markov模型(简称MM2).MM2模型假设一个位置的辅助信息屏蔽了其他位置辅助信息对该位置主要信息的影响.实验结果表明,当主要信息定义在比辅助信息小的空间尺度时,COSGSIM方法在MM2模型下比MM1有效.

Abstract: Reconstruction always uses some kinds of interpolation methods and its accuracy can be improved by using multiple data with different dimensions, resolutions or types. COSGSIM (sequential Gaussian co-simulation) has been a widely used geostatistical interpolation method and is introduced into other fields for prediction and reconstruction in recent years because it can estimate unknown values by multiple known data including known primary data (hard data) and some auxiliary data (soft data). The LMC (linear model of coregionalization) and the original MM1 (Markov model 1) are proposed for COSGSIM to fulfill the integration of the primary data and auxiliary data. The main limitation of LMC is the requirement of modeling a positive definite cross covariance matrix for different variables. MM1 is a reasonable model only when the primary data are defined on the larger volume support than the auxiliary data. Then MM2 (Markov model 2) for such a case is presented to meet the above condition in an improved Markov model. MM2 screening hypothesis indicates that an auxiliary datum screens the influence of any other auxiliary datum on its primary collocated datum. Experimental results show that the interpolated results of COSGSIM under MM2 are much better than those of COSGSIM under MM1 if the primary data are defined on a larger volume support.

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