An orthogonal series density estimation approach to reconstructing positron emission tomography images

Positron emission tomography (PET) is an important medical imaging technique. Statistically, the PET image reconstruction problem comprises estimating the intensity function of a non-homogeneous Poisson process from a set of indirectly observed data (an integral transform is involved). In this paper, we investigate a new reconstruction method consisting in the adaptation of orthogonal series density estimation techniques to use with an idealised form of the PET problem. The method provides reasonable reconstructions quickly; its computational speed is its major advantage. It has further advantages (e.g. no pixellation required) and various disadvantages (e.g. difficulties with object boundaries, non-negativity not guaranteed) which are discussed. Its major disadvantage, however, is the difficulty associated with generalising the approach to cope with more realistic versions of the PET model.