Alternating update penalized-likelihood image reconstruction for x-ray fluorescence computed tomography

In this work, we continue to pursue penalized-likelihood image reconstruction algorithms for X-ray fluorescence computed tomography (XFCT) when the attenuation maps at the energies of the fluorescence X-rays are unknown. Our previous approach, while yielding good results, was somewhat heuristic and did not necessarily correspond to maximization of a predefined penalized-likelihood objective function. Here we present an iterative algorithm that is guaranteed to increase a predefined objective function at each iteration. The approach alternates between updating the distribution of a given element and updating the attenuation map for that element's fluorescence X-rays. We apply the algorithm to simulated numerical data as well as to real synchrotron data.