Optimization-based multiple-point geostatistics: A sparse way

In multiple-point simulation the image should be synthesized consistent with the given training image and hard conditioning data. Existing sequential simulation methods usually lead to error accumulation which is hardly manageable in future steps. Optimization-based methods are capable of handling inconsistencies by iteratively refining the simulation grid. In this paper, the multiple-point stochastic simulation problem is formulated in an optimization-based framework using a sparse model. Sparse model allows each patch to be constructed as a superposition of a few atoms of a dictionary formed using training patterns, leading to a significant increase in the variability of the patches. To control the creativity of the model, a local histogram matching method is proposed. Furthermore, effective solutions are proposed for different issues arisen in multiple-point simulation. In order to handle hard conditioning data a weighted matching pursuit method is developed in this paper. Moreover, a simple and efficient thresholding method is developed which allows working with categorical variables. The experiments show that the proposed method produces acceptable realizations in terms of pattern reproduction, increases the variability of the realizations, and properly handles numerous conditioning data. HighlightsA new optimization-based MPS simulation method.The first effort to apply sparse models to multiple-point geostatistics.Weighted matching pursuit method is proposed for handling conditioning data.Histogram-based thresholding is proposed for handling categorical variables.Combining a few patches leads to an increased variability.