Abstract: 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.

Abstract: We provide improved maximum likelihood expectation maximization (MLEM) joint estimation of emission activity and photon attenuation from positron emission tomography (PET) data. Lines of response (LOR) are divided along their length into cells having equal length. MLEM computations assume all intersections between LOR cells and voxels have an intersection length of the LOR cell length. This way of discretizing the problem has the significant advantage of leading to MLEM update equations that have a closed form exact solution, which is important for fast, accurate and robust estimation.

Abstract: We provide improved maximum likelihood expectation maximization (MLEM) joint estimation of emission activity and photon attenuation from positron emission tomography (PET) data. Lines of response (LOR) are divided along their length into cells having equal length. MLEM computations assume all intersections between LOR cells and voxels have an intersection length of the LOR cell length. This way of discretizing the problem has the significant advantage of leading to MLEM update equations that have a closed form exact solution, which is important for fast, accurate and robust estimation.

Abstract: 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.