Analysis on Fourier-based inversion methods for 3D-PET reconstruction

Due to the physical nature of annihilation process, 3D imaging techniques are intrinsically demanded for the positron emission tomography (PET). However, the incorporation of additional cross-plane measurements imposes excessive amount of projection data and thereby clinically impractical reconstruction time. For this reason, Fourier-based inversion methods deserve a deepening investigation. The crucial parts of such methods are the interpolation procedures in frequency domain which always associate with inaccuracies. In this paper, both a direct approach based on linear averaging (inverse distance weighting method) and an indirect approach based on two-dimensional convolution (gridding method) are analyzed. In particular, two significant aspects of the gridding method are paid attention to. The first aspect is the choice of applied two-dimensional convolution function, whereas the second is the discretization of continuous convolution. For the latter aspect, geometrical structure named Voronoi diagram and its computational construction have to be discussed. In the end, results of performed simulation studies are presented.