A model problem for restricted-data gamma ray emission tomography of highly active nuclear waste

This paper develops the work of Cattle et al. [Cattle, B.A., Fellerman, A.S., West, R.M., 2004. On the detection of solid deposits using gamma ray emission tomography with limited data. Measurement Science and Technology 15, 1429-1439] by considering a generalization of the model employed therein. The focus of the work is the gamma ray tomographic analysis of high-level waste processing. The work in this paper considers a two-dimensional model for the measurement of gamma ray photon flux, as opposed to the previous one-dimensional analysis via the integrated Beer-Lambert law. The mathematical inverse problem that arises in determining physical quantities from the photon count measurements is tackled using Bayesian statistical methods that are implemented computationally using a Markov chain Monte Carlo (MCMC) approach. In a further new development, the effect of the degree of collimation of the detector on the reliability of the solutions is also considered.