Spatial Interpolation and Conditional Map Generation Using Deep Image Prior for Environmental Applications

Kriging is the most widely used spatial interpolation method in geostatistics. For many environmental applications, kriging may have to satisfy the stationarity and isotropy hypothesis, and new techniques using machine learning suffer from a lack of labeled data. In this paper, we propose the use of deep image prior, which is a U-net-like deep neural network designed for image reconstruction, to perform spatial interpolation and conditional map generation without any prior learning. This approach allows us to overcome the assumptions for kriging as well as the lack of labeled data when proposing uncertainty and probability above a certain threshold. The proposed method is based on a convolutional neural network that generates a map from random values by minimizing the difference between the output map and the observed values. With this new method of spatial interpolation, we generate n maps to obtain a map of uncertainty and a map of probability of exceeding the threshold. Experiments demonstrate the relevance of the proposed methods for spatial interpolation on both the well-known digital elevation model data and the more challenging case of pollution mapping. The results obtained with the three datasets demonstrate competitive performance compared with state-of-the-art methods.