Maximum Likelihood Expectation-Maximization (MLEM) is a popular algorithm to reconstruct the activity image in Positron Emission Tomography (PET). This paper introduces a 'fundamental equality' for the MLEM complete data from which two key properties easily follow that allows us to: (i) prove in an elegant and compact way the convergence of MLEM for a forward model with fixed background (i.e., counts such as random and scatter coincidences); and (ii) generalize this proof for the MLEM-3 algorithm. Moreover we give necessary and sufficient conditions for the solution to be unique.

Original languageEnglish
Pages (from-to)721-729
Number of pages9
JournalIEEE Transactions on Medical Imaging
Issue number3
Early online date18 Sep 2018
Publication statusPublished - Mar 2019

    Research areas

  • Convergence, Data models, Image reconstruction, Image Reconstruction, Maximum likelihood estimation, Positron emission tomography, Positron Emission Tomography (PET)

ID: 39605551