Reconstruction of Incomplete Data Sets orImages Using Direct Sampling

Mariethoz, Gregoire ; Renard, Philippe

In: Mathematical Geosciences, 2010, vol. 42, no. 3, p. 245-268

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    With increasingly sophisticated acquisition methods, the amount of data available for mapping physical parameters in the geosciences is becoming enormous. If the density of measurements is sufficient, significant non-parametric spatial statistics can be derived from the data. In this context, we propose to use and adapt the Direct Sampling multiple-points simulation method (DS) for the reconstruction of partially informed images. The advantage of the proposed method is that it can accommodate any data disposition and that it can indifferently deal with continuous and categorical variables. The spatial patterns found in the data are mimicked without model inference. Therefore, very few assumptions are required to define the spatial structure of the reconstructed fields, and very limited parameterization is needed to make the proposed approach extremely simple from a user perspective. The different examples shown in this paper give appealing results for the reconstruction of complex 3D geometries from relatively small data sets