Novel Method of Tensor Representation for Reconstruction of 3-D PET Images From Projections

摘要

In this paper, a novel transform-based method of reconstruction of three-dimensional (3-D) positron emission tomography (PET) images is proposed. The proposed method is based on the concept of the non-traditional tensor form of representation of the 3-D image with respect to the 3-D discrete Fourier transform (DFT). Such representation uses a minimal number of projections. The proposed algorithms are described in detail for an image (N x N x N), where N is a power of two. The paired transform is defined completely by projections along the discrete grid nested on the image domain. The measurement data set containing specified projections of the 3-D image are generated according to the tensor representation and the proposed algorithm is tested on the data. The algorithm for selecting a required number of projections is described. This algorithm allows the user to select the projections that contain the maximum information and automatically selects the rest of the projections, so that there is no redundancy in the spectral information of the projections.