An MLEM method for joint tissue activity distribution and photon attenuation map reconstruction in PET

A Maximum Likelihood Expectation Maximization (MLEM) method is proposed for joint tissue activity distribution and photon attenuation map reconstruction from Positron Emission Tomography (PET) data. It is based on a new set of latent random variables, similar to the ones used by Lange and Carson for CT [JCAT, 1984]. It results in a separable likelihood function, which simplifies maximization. The proposed method is consistent with the methods of Krol et al. for SPECT [TMI, 2001] and Shepp and Vardi for PET [TMI, 1982].