Evaluation of frequency-distance relation validity for FORE optimization in 3D PET

Fourier rebinning (FORE) is the most widely used rebinning algorithm to reorganize 3-D PET data into 2-D sinograms. In Fourier transform (FT) domain, data from oblique sinograms are assigned to transaxial ones at a proper axial displacement given by the frequency-distance relation. Approximation accuracy falls at low frequencies, where only low-copolar angles can be exploited by means of single slice rebinning (SSRB). Usually, an abrupt partition by a square region centered on DC is applied, which does not weight accuracy in the sinogram FT domain and copolar angle dependence, and can introduce artifacts due to the sharp transition. In this work we propose a simple index which maps the frequency-distance relation validity in the sinogram FT domain. Two new criteria were tested on this basis: 1) an abrupt transition based on validity map contours and 2) a gradual transition following the monotonical validity increase with frequency. In both criteria copolar angle dependence was introduced. Standard, abrupt, and gradual partitions were compared on different phantoms acquired with ECAT EXACT HR+ scanner, characterized by a large span = 9 (saved sinograms group 4 or 5 acquired sinograms, by averaging) and by a low maximum copolar angle (6°). In this condition the methods provided similar tradeoffs of SNR optimization against blur and artifact appearance, thus confirming the validity of the frequency-distance relation at low copolar angles. A simulation study emulating an hypothetical scanner with span = 3 and larger acceptance copolar angle (25.5°) conversely showed more clear improvements