A novel information reconstruction method using an improved COSGSIM model

Information reconstruction always uses some kinds of interpolation methods and its accuracy can be improved by using multiple data with different dimensions, resolutions or types. Sequential Gaussian co-simulation (COSGSIM) has been a widely used geostatistical interpolation method and is introduced into other fields for prediction and reconstruction in recent years, which can estimate unknown values by multiple known data including the actual measured data and vaguely evaluated data represented respectively by a primary variable and a secondary variable. The linear model of coregionalization (LMC) and the Markov model 1 (MM1) were proposed for COSGSIM and some other interpolation methods to fulfill the integration of the primary variable and the secondary one. The main limitation of LMC is the requirement of modeling a positive definite cross covariance matrix for both primary and secondary variables, which cannot easily be solved by original COSGSIM. Although MM1 is a reasonable model if the primary variable is defined on the same or a larger volume support than the secondary one, allowing it to screen the influence of further away data of the primary variable, consider the case of a secondary variable defined on a much larger support than the primary variable, the MM1 is not appropriate. Then Markov model 2 (MM2) for such a case is presented to meet the above condition in an improved COSGSIM model. The new MM2 screening hypothesis indicates that the soft (secondary) datum screens the influence of any other soft datum on its hard (primary) collocated datum, which leads to the approximation for the COSGSIM. Experimental results show that the reconstructed results of COSGSIM under MM2 are much better than those of COSGSIM under MM1.