Poisson and Bayesian Estimation of Low Signal Source and Noise Components

Abstract

Mobile radiation detectors aim to help identify sources of radiation. Finding a radioactive source in a man-made environment such as a city can be challenging because the additive signal received by the detector contains both photon counts from the source of interest and from the cluttered and variable ambient background. Decomposing the overall radiation spectrum into its background and source signal components is key. When either or both of the background or source components is low in photon counts, the estimation of signal components can become especially challenging. Gamma-ray spectrometry data is typically presumed to be created with a Poisson process, though Gaussian-based estimators are typically used to approximate the truly Poisson-distributed data. Generally this approximation suffices, but performance loss can occur when photon counts affecting a sensor are low in number for any signal component. Low photon count signal and/or noise components can occur in a variety of real world scenarios. Photon counts from the source may be low because the source is very weak or only observable from large standoff distances. Photon count rate from both source and background may be low if small sensors (with limited surface area) are used or if measurement time is limited. Our study experiments with augmenting established anomaly detection and match filter signal component estimators with Poisson-based models. We apply estimators such as the Poisson Principal Component Analysis (Poisson PCA) and the Zero- Inflated Poisson (ZIP) models to the source detection problem and benchmark with respect to popular estimators in the literature. Finally, we apply Bayesian Aggregation to the Poisson-based estimators to aggregate evidence across multiple spatially-correlated sensor observations. Our results indicate that the use of such techniques can aid threat detection when photon counts are low in signal and/or background noise components.