Improving spatial interpolation for anomaly analysis in presence of sparse, clustered or imprecise data sets

Abstract

In this study, we present a new method of interpolation and anomaly detection especially designed for sparse, clustered or imprecise environmental data (SIC). Such data cannot be processed by current state of the art spatial methods and models, including the most widely used, such as kriging. Indeed, the statistics obtained on SIC data (on the order of 5–30) do not allow us to define a covariance or to calibrate the numerous hyper-parameters of sophisticated Bayesian or deep image prior models. We therefore adapted an information dissemination algorithm to handle SIC data. This probabilistic model has been enriched (anisotropy, de-clustering, auto-variography, multi-support, treatment of covariates, and censored data) in a way that fully meets the needs for environmental SIC data and can be used in conjunction with hybrid propagation of epistemic and aleatoric uncertainties and anomaly detection, whatever their mathematical form. The new interpolator for anomaly detection was applied on a very small set of 13 sparse data points characteristic of small-scale environmental studies, on digital-challenge datasets and on two real datasets, i.e., a large-scale geochemical dataset and a SIC urban soil dataset. Results highlight the added value of the proposed algorithm, that is able to pinpoint anomalies in SIC data, while avoiding in particular the smoothing effects of certain previous methods.