PET image reconstruction with rotationally symmetric polygonal pixel grid based highly compressible system matrix

To achieve a maximum compression of system matrix in positron emission tomography (PET) image reconstruction, we proposed a polygonal image pixel division strategy in accordance with rotationally symmetric PET geometry. Geometrical definition and indexing rule for polygonal pixels were established. Image conversion from polygonal pixel structure to conventional rectangular pixel structure was implemented using a conversion matrix. A set of test images were analytically defined in polygonal pixel structure, converted to conventional rectangular pixel based images, and correctly displayed which verified the correctness of the image definition, conversion description and conversion of polygonal pixel structure. A compressed system matrix for PET image recon was generated by tap model and tested by forward-projecting three different distributions of radioactive sources to the sinogram domain and comparing them with theoretical predictions. On a practical small animal PET scanner, a compress ratio of 12.6:1 of the system matrix size was achieved with the polygonal pixel structure, comparing with the conventional rectangular pixel based tap-mode one. OS-EM iterative image reconstruction algorithms with the polygonal and conventional Cartesian pixel grid were developed. A hot rod phantom was detected and reconstructed based on these two grids with reasonable time cost. Image resolution of reconstructed images was both 1.35 mm. We conclude that it is feasible to reconstruct and display images in a polygonal image pixel structure based on a compressed system matrix in PET image reconstruction.