ML-reconstruction for TOF-PET with simultaneous estimation of the attenuation factors

In positron emission tomography (PET), attenuation correction is typically done based on information obtained from transmission tomography. Recently, it has been shown that stable maximum-likelihood reconstruction of both the attenuation and the activity from time-of-flight (TOF) PET emission data is possible. Mathematical analysis revealed that the TOF-PET data determine the attenuation correction factors uniquely except for a scale factor. Here, we propose a maximum likelihood algorithm (called MLACF) that jointly estimates the image of the activity distribution and the sinogram with the attenuation factors. This method avoids the reconstruction of the attenuation image. If additive contributions (such as scatter and randoms) can be ignored, the algorithm even does not require storage of the attenuation correction factors. However, in contrast, this algorithm does not impose the consistency of the attenuation sinogram, which may result in increased noise propagation. This paper presents the derivation of the algorithm, an (incomplete) theoretical analysis of the corresponding likelihood function, and first results on 2D and 3D simulations.