Joint activity and attenuation estimation for PET with TOF data and single events

Abstract

Maximum likelihood reconstruction of activity and attenuation (MLAA) for PET data with time-of-flight (TOF) information can determine the activity distribution up to a scale, and the attenuation map Radon transform up to a related constant. Prior knowledge is widely used for the determination of the constant. However, prior knowledge could be inaccurate due to patient variation and may result in quantitation errors. Our goal is to develop a method that can determine the scale and the related constant in the TOF-MLAA algorithm to obtain quantitatively accurate activity and attenuation maps.Our idea is to utilize the single events which have depth dependent attenuation factors, contrary to coincidence events. We show that in a 2D case, with the combination of TOF information and single events, a unique solution of attenuation and activity can be achieved. A three-step iterative image reconstruction algorithm is developed. In each iteration, the activity distribution is first updated using the MLEM approach with TOF PET data; the attenuation map is then updated using MLTR with non-TOF data; finally, both activity distribution and attenuation map are updated using a scale estimated from single events. Noisy and noise-free projection data are generated for 2D XCAT phantoms through analytical simulation. Both scatter information and randoms information are assumed to be known. The proposed method and the conventional TOF-MLAA algorithm are used to reconstruct the simulated data. Conventional MLEM method with known attenuation map is implemented for comparison as well. Normalized root mean square error (NRMSE) and optimal constant are defined for the quantitative analysis of reconstructed images. Our proposed image reconstruction method achieves ~1% NRMSE for the activity map and ~5% NRMSE for the attenuation map with a correct scale after 150 iterations for noise-free data. Results of noisy simulations are consistent with noise-free data.In summary, we have proposed to use the single events for constant determination in TOF-MLAA algorithm to obtain a unique solution of attenuation map and activity distribution without prior information. Future work will be dedicated to the extension of our method to the 3D situation.