Maximum likelihood activity and attenuation estimation using both emission and transmission data with application to utilization of Lu-176 background radiation in TOF PET

Purpose We present a new method for joint reconstruction of activity and attenuation images using both emission and transmission data and demonstrate its advantage over the standard maximum likelihood activity and attenuation (MLAA) reconstruction using emission data alone. Methods We define a joint likelihood function including both time-of-flight (TOF) emission data and transmission data. The latter can be obtained from an external source or from Lu-176 background radiation. Activity and attenuation images are estimated jointly by maximizing the likelihood function. The proposed method solves the undetermined scale problem in the conventional MLAA. A monotonically convergent algorithm was derived to optimize the objective function. Furthermore, we present a theoretical analysis of the noise propagation in the joint reconstruction. Simulations and phantom experiments were conducted to validate the feasibility of the proposed method. Results Quantitatively correct and less noisy images were reconstructed with the proposed method. Artifacts in the attenuation map reconstructed from the standard MLAA were removed by incorporating transmission data. Noise analysis was validated with different transmission sources and transmission count levels. The theoretical prediction indicated that noise of activity map would not change in a large range of transmission count level and a very low transmission count level could result in good estimation. Conclusions The results demonstrate the feasibility of obtaining quantitatively correct images in TOF PET by using both emission and (weak) transmission data. The noise analysis also provides guidance for choosing a proper transmission source configuration to reduce noise propagation.