Stochastic reconstruction of spatial data using LLE and MPS

Spatial data are widely used in many scientific and engineering fields, such as remote sensing, environment monitoring, weather forecast and mineral exploitation. However, direct measurements of such spatial data sometimes are difficult to achieve due to the expensive cost of equipment or current limited technology, so stochastic reconstruction or simulation of spatial data are necessary based on the principles of statistics. As a typical statistical modeling method, multiple-point statistics (MPS) has been successfully used for stochastic reconstruction by reproducing the features from training images (TIs) to the reconstructed regions. However, because these features mostly have intrinsic nonlinear relations, the traditional MPS methods using linear dimensionality reduction are not suitable to deal with the nonlinear situation. In this paper a new method using locally linear embedding (LLE) and MPS is proposed to resolve this issue. As a classical nonlinear method of dimensionality reduction in manifold learning, LLE is combined with MPS to reduce redundant data of TIs so that the subsequent reconstruction can be faster and more accurate. The tests are performed in both 2D and 3D reconstructions, showing that the reconstructions can reproduce the structural features of TIs and the proposed method has its advantages in reconstruction speed and quality over typical methods using linear dimensionality reduction.