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.