Method of reconstruction of 3-D pet images from projections

In this paper, a novel method of reconstruction of 3-D Positron Emission Tomography (PET) images is proposed. The method is based on the concept of non traditional, tensor and paired forms of representation of the 3-D image with respect to the 3-D discrete Fourier transform (DFT). Such representations use a minimal number of projections. The proposed algorithm is described in detail for an image (N × N × N), where N is a power of two. A multi-ring scanner that has contiguous rings of detectors stacked on top of each other is considered. The measurement data set containing specified projections of the 3-D image are generated according to the paired representation, and the proposed algorithm is tested on the data. The algorithm for selecting a required number of projections is described and illustrated for image (32×32×32).