Analytic reconstruction of the attenuation from 3D time-of-flight PET data

Abstract

In positron emission tomography (PET), an accurate quantitative reconstruction of the tracer distribution requires taking into account the attenuation of the photons by the tissues. The spatial distribution of the attenuation coefficient (the attenuation image) is usually estimated by means of a CT scan, extrapolated to the required photon energy of 511 keV and forward projected to obtain the attenuation sinogram [1]. We consider applications where this external information about the attenuation is unavailable, or inaccurate due for instance to patient motion between the transmission scan and the emission scan. In such a case the attenuation must be estimated from the emission data only. Previous studies [2]–[4] have shown that time-of-flight (TOF) data contain significant information on the attenuation. Recently, we proved that the attenuation sinogram is determined, up to a constant multiplicative factor, by the 2D TOF data and that it can be calculated using an efficient analytic algorithm [5]. This paper extends this work to 3D TOF PET. Iterative algorithms dealing with the same problem are presented in [6]–[10].