Sampling requirements of projection signals in 3D PET

In this paper the spectral properties of projection signals of 3D PET are analyzed. In particular, under the application of the 3D version of Fourier slice theorem, the inhomogeneous spatial distribution of frequency samples in the reconstructed 3D object spectrum is clarified. The analysis also reveals the fact that the 3D operating mode of a PET scanner is actually only a pseudo-3D measuring mode. Distinct regions in the reconstructed object spectrum benefit differently from the additional so-called cross-plane measurements. Due to the existence of redundancy in the 4D projection signals of the 3D PET, no means exists to establish an accurate and uniform sampling grid for the projection signal. To overcome this burden, an alternative form of projection as integral over planes is introduced. Based on the sampling pattern acquired for these new projection signals, approximate assertions can be made concerning the sampling requirements for the projection of 3D PET.