When reconstructing spatial data

if conditional data are sparse or even not existent

reconstructed results often show a lot of uncertainties

so it is appropriate to use stochastic simulation based on statistical theories to reconstruct spatial data. As one of the main stochastic simulation methods

multiple-point statistics (MPS) can copy the intrinsic features extracted from training images to the reconstructed regions. Because the traditional MPS methods using linear dimensionality reduction cannot effectively handle nonlinear data but locally linear embedding (LLE) can achieve dimensionality reduction of nonlinear data

an indefinite reconstruction method using LLE and MPS for spatial data is proposed. The experimental results for images show that the proposed method is practical.