Geological Field Restoration through the Lens of Image Inpainting

We present a new viewpoint on a reconstructing multidimensional geological fields from sparse observations. Drawing inspiration from deterministic image inpainting techniques, we model a partially observed spatial field as a multidimensional tensor and recover missing values by enforcing a global low-rank structure. Our approach combines ideas from tensor completion and geostatistics, providing a robust optimization framework. Experiments on synthetic geological fields demonstrate that used tensor completion method significant improvements in reconstruction accuracy over ordinary kriging for various percent of observed data.