The article is devoted to a further study of the Compton camera method of passive detection of small amounts of special nuclear materials, developed by the authors in their previous work. Various cargo scenarios, detector errors, and other issues are addressed.
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 re
ach 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.
The paper surveys recent progress in establishing uniqueness and developing inversion formulas and algorithms for the thermoacoustic tomography. In mathematical terms, one deals with a rather special inverse problem for the wave equation. In the case
of constant sound speed, it can also be interpreted as a problem concerning the spherical mean transform.
