Maximum-a-Posteriori Cosmic Ray Muon Trajectory Estimation with Energy Loss for Muon Tomography Applications

Recent cosmic ray muon tomography applications use detectors that measure position and direction of the individual muons before and after traversing the imaged object. However, muon reconstruction techniques are limited in resolution due to low muon flux and the effects of a single Coulomb scattering assumption. In the present work, the use of a Bayesian framework and a Gaussian approximation of multiple Coulomb scattering (MCS) is explored for maximum-a-posteriori estimation of the most likely path of a cosmic ray muon traversing a uniform and nonuniform medium and undergoing MCS. Results were generated using a validated Geant4 workspace. The algorithm is expected to he able to predict muon tracks with improved accuracy and to increase the useful muon flux by 30% over a traditional point-of-closest-approach (PoCA) method. The effect of energy loss due to ionization is investigated, and an energy loss relation is derived and validated.