Reconstruction of spatial data using isometric mapping and multiple-point statistics

Only partial spatial information in studied fields is a ubiquitous problem in the reconstruction of spatial data and is the major cause of uncertainty for reconstructed results. This is not likely to change since there will always be some unsampled volumes in the simulated regions where no direct information is available. Multiple-point statistics (MPS) can be a powerful tool to address this issue because it can extract the features of training images and copy them to the simulated regions using sparse conditional data or even without any conditional data. Because the data from training images are not always linear, previous MPS methods using linear dimensionality reduction are not suitable to deal with nonlinear situation. A new method using MPS and isometric mapping (ISOMAP) that can achieve nonlinear dimensionality reduction is proposed to reconstruct spatial data. The patterns of the training image are classified using a clustering method after the dimensionality is reduced. The simulation of patterns is performed by comparing the current data event and the average of all classified patterns in a class and finding out the one most similar to the current data event. The experiments show that the structural characteristics of reconstructions using the proposed method are similar to those of training images.