sMLACF: a generalized expectation-maximization algorithm for TOF-PET to reconstruct the activity and attenuation simultaneously

The 'simultaneous maximum-likelihood attenuation correction factors' (sMLACF) algorithm presented here, is an iterative algorithm to calculate the maximum-likelihood estimate of the activity λ and the attenuation factors a in time-of-flight positron emission tomography, and this from emission data only. Hence sMLACF is an alternative to the MLACF algorithm. sMLACF is derived using the generalized expectation-maximization principle by introducing an appropriate set of complete data. The resulting iteration step yields a simultaneous update of λ and a which, in addition, enforces in a natural way the constraints ##IMG## [http://ift.tt/2xB3M7U] {$ \newcommand{\e} {\epsilon \leqslant a \leqslant 1}$} where ##IMG## [http://ift.tt/2yjtKR2] {$ \newcommand{\e} {0 < \epsilon < 1}$} is a fixed lower boun...

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