Data sampling in multislice mode PET for multi-ring scanner

The aim of this work is to use sampling theory to guide mashing schemes in multislice mode (2D) PET for multi-ring scanners. We adapt previous work on fan beam sampling to PET geometry. It results in a change of the shape of the essential support of the Fourier transform of the 3D fan beam X-ray transform. The use of square detectors in 2D multi-ring PET induces an oversampling in the transverse plane. A mashing scheme is therefore suggested to make profit of the oversampling in order to produce an efficient hexagonal sampling scheme. We add in average 24.5 LORs to form one single barycentric LOR according to a specific mashing scheme in each transverse plane. Thus, the number of LORs is significantly reduced while satisfying the hexagonal sampling conditions. Although this process causes a loss of resolution, the proposed mashing scheme optimises the trade-off between data compression and resolution.