Characterization of tomographic sampling in hybrid-PET using the Fourier crosstalk matrix

Summary form only received as follows: Hybrid PET systems can be used to measure the distribution of positron emitting radionuclides. An important focus for Hybrid PET is to determine the tomographic sampling requirements. Barrett et al. (J. Opt. Soc. Am. 1995) have previously developed a theoretical formulation for quantifying sampling in continuous-to-discrete tomographic systems. This tool, the crosstalk matrix, provides information on the recoverability of the Fourier coefficients that represent the continuous object. In addition, the crosstalk matrix can be related to image quality assessment. In this study, the crosstalk matrix was used to evaluate sampling in two- (heads separated by 180 degrees) and three-head (heads separated by 120 degrees) Hybrid PET systems. The emphasis was on evaluating the effect of angular sampling on system performance. For both geometries, performance was evaluated for 1,2, and a large number of gantry stops (complete sampling). The crosstalk matrix diagonals (analogous to the system MTF) demonstrate that increased sampling improves Fourier coefficient recoverability. The Cramer-Rao bound (CRB) for estimating the unknown Fourier coefficients of the object was also computed. The CRB was higher for Fourier coefficients of high spatial frequency. Overall, the CRB for complete sampling was lower than with one or two gantry stops.