Multiscale spatial density smoothing: an application to large-scale radiological survey and anomaly detection

TL;DR

This paper introduces a multiscale spatial density smoothing method tailored for large-scale radiological surveys, effectively handling complex spatial features and data sparsity to improve anomaly detection accuracy.

Contribution

The paper presents a novel multiscale smoothing approach that addresses non-stationary, non-isotropic spatial correlations and sparse data in density estimation tasks.

Findings

State-of-the-art spatial smoothing performance

Enhanced anomaly detection power

Effective handling of complex spatial features

Abstract

We consider the problem of estimating a spatially varying density function, motivated by problems that arise in large-scale radiological survey and anomaly detection. In this context, the density functions to be estimated are the background gamma-ray energy spectra at sites spread across a large geographical area, such as nuclear production and waste-storage sites, military bases, medical facilities, university campuses, or the downtown of a city. Several challenges combine to make this a difficult problem. First, the spectral density at any given spatial location may have both smooth and non-smooth features. Second, the spatial correlation in these density functions is neither stationary nor locally isotropic. Finally, at some spatial locations, there is very little data. We present a method called multiscale spatial density smoothing that successfully addresses these challenges. The method is based on recursive dyadic partition of the sample space, and therefore shares much in common with other multiscale methods, such as wavelets and P\'olya-tree priors. We describe an efficient algorithm for finding a maximum a posteriori (MAP) estimate that leverages recent advances in convex optimization for non-smooth functions. We apply multiscale spatial density smoothing to real data collected on the background gamma-ray spectra at locations across a large university campus. The method exhibits state-of-the-art performance for spatial smoothing in density estimation, and it leads to substantial improvements in power when used in conjunction with existing methods for detecting the kinds of radiological anomalies that may have important consequences for public health and safety.