Statistical Image Reconstruction for Muon Tomography Using a Gaussian Scale Mixture Model

Muon tomography is a novel imaging technique that uses background cosmic radiation to inspect vehicles or cargo containers for detecting the transportation or smuggling of heavy nuclear materials. Empirically, muon scattering data are modeled as zero-mean Gaussian random variables with variance being a function of the atom number and density of the scattering material. However, a single Gaussian distribution cannot model the tail of the true distribution and hence results in noisy reconstructed images. In this paper, we propose a Gaussian scale mixture (GSM) to approximate the true distribution of muon data. The GSM follows the true distribution more closely than a single Gaussian model. We have derived a maximum a posteriori (MAP) reconstruction algorithm based on the GSM likelihood. Localization receiver operating characteristics (LROC) studies were performed using computer simulated data to evaluate the new algorithm. The results show that the use of GSM improves the detection performance significantly over that of the traditional Gaussian likelihood.