In the radiological characterisation of nuclear power stations, gamma spectroscopy builds the basis for many further investigation methods. The measurements of scintillation detectors in, e.g. a Compton camera, can be used to identify a priori the present radioactive nuclides. We formulate this gamma spectrum analysis problem as a Bayesian inverse problem with Poisson-distributed data. Techniques from convex analysis are used to compute the resulting maximum likelihood estimator given by a list of present nuclides and their corresponding intensities. The approach is tested on coincidence data measured with a Compton camera in potential use cases.

Compton cameras are stationary, uncollimated gamma ray imaging devices that use the Compton effect to reconstruct a spatially resolved activity distribution. Due to the missing collimation, the cameras exhibit high sensitivities, particularly so for setups with large detectors in close distance of each other. This allows reconstruction in relatively low-count regimes and hence a flexible application in areas of low activity. For cameras with spatially non-resolved detectors, the size of the detectors however results in large angular uncertainty and distorted measurements due to multiple scattering contributions in the data. In this talk, we address the design and corresponding modeling approaches of Compton cameras with such monolithic, spatially non-resolved scintillation detectors. Numerical results on measured data support the theoretical considerations.

Compton cameras have a long tradition in $\gamma$-ray astronomy and increasingly find new applications in radiation protection and nuclear safety. We have built three prototypes of Compton cameras to assist the decommissioning process of safely removing a nuclear facility from service and reducing residual radioactivity to permissible levels. In this talk, the inverse problem of Compton cameras is addressed with two techniques, one based on a Bayesian framework, and another graph-based approach that makes full use of the discrete nature of ionizing radiation interactions with matter. We have implemented a new physics concept in our Compton cameras whereby we no longer label radiation detectors according to their function as either scattering or absorbing detectors but rather characterize them by their materials, most importantly their effective atomic number $Z_\text{eff}$. As essentially no detector exists that would exclusively absorb radiation, we propose to record coincidence events between all pairs of detectors in which at least one detector material has $Z_\text{eff} > 30$. This new trigger condition includes coincidences of detector pairs where both materials have $Z_\text{eff} > 30$ which would traditionally be labeled absorbing detectors and would normally not be recorded by a Compton camera. These changes in the electronics setup of our Compton cameras yield an enlarged data sample available for subsequent inversion treatment.

We will present experimental results obtained with the relevance vector machine and a graph heuristic used for assigning coincidence events to emission points. The measurements were carried out at the radiation laboratory of the University of Applied Sciences Zittau/Görlitz. We gratefully acknowledge financial support by the Federal Ministry of Education and Research (BMBF) through the FORKA program under Grant No. 15S9431A-D.