A method of PET image reconstruction is provided that includes obtaining intra-patient tissue activity distribution and photon attenuation map data using a PET/MRI scanner, and implementing a Maximum Likelihood Expectation Maximization (MLEM) method in conjunction with a specific set of latent random variables, using an appropriately programmed computer and graphics processing unit, wherein the set of latent random variables comprises the numbers of photon pairs emitted from an electron-positron annihilation inside a voxel that arrive into two given voxels along a Line of Response (LOR), where the set of latent random variables results in a separable joint emission activity and a photon attenuation distribution likelihood function.
