Joint Activity and Attenuation Reconstruction from Multiple Energy Window Data with Photopeak Scatter Re-Estimation in Non-TOF 3-D PET

Estimation of attenuation from positron emission tomography (PET) data only is of interest for hybrid PET-MR and systems where CT is not available or recommended. However, when using data from a single energy window, emission-based non-time-of-flight (TOF) PET attenuation correction (AC) methods suffer from 'cross-talk' artifacts. Based on earlier work, this article explores the hypothesis that cross-talk can be reduced by using more than one energy window. We propose an algorithm for the simultaneous estimation of both activity and attenuation images, as well as, the scatter component of the measured data from a PET acquisition, using multiple energy windows. The model for the measurements is 3-D and accounts for the finite energy resolution of PET detectors; it is restricted to single scatter. The proposed energy-based simultaneous maximum likelihood reconstruction of activity and attenuation with photopeak scatter re-estimation algorithm is compared with simultaneous estimation from a single energy window simultaneous maximum likelihood reconstruction of activity and attenuation with photopeak scatter re-estimation. The evaluation is based on simulations using the characteristics of the Siemens mMR scanner. Phantoms of different complexity were investigated. In particular, a 3-D XCAT torso phantom was used to assess the inpainting of attenuation values within the lung region. Results show that the cross-talk present in non-TOF maximum likelihood reconstruction of activity and attenuation reconstructions is significantly reduced when using multiple energy windows and indicate that the proposed approach warrants further investigation.