A Bayesian Approach to Detection of Small Low Emission Sources

TL;DR

This paper presents a Bayesian method using MCMC for detecting and locating small low-emission sources within objects amid high background noise, relevant for homeland security applications.

Contribution

It introduces a Bayesian framework with Bayes factors and MCMC to detect and locate low emission sources, achieving effective results at low SNR levels.

Findings

Method can detect sources at SNR levels around 10^{-3}

Bayesian approach provides both detection and localization

Simulation confirms effectiveness with high emission levels

Abstract

The article addresses the problem of detecting presence and location of a small low emission source inside of an object, when the background noise dominates. This problem arises, for instance, in some homeland security applications. The goal is to reach the signal-to-noise ratio (SNR) levels on the order of $10^{-3}$. A Bayesian approach to this problem is implemented in 2D. The method allows inference not only about the existence of the source, but also about its location. We derive Bayes factors for model selection and estimation of location based on Markov Chain Monte Carlo (MCMC) simulation. A simulation study shows that with sufficiently high total emission level, our method can effectively locate the source.