A new convergent MAP reconstruction algorithm for emission tomography using ordered subsets and separable surrogates

We investigate a new, fast and provably convergent MAP reconstruction algorithm for emission tomography. The new algorithm, termed C-OSEM has its origin in the alternating algorithm derivation of the well known EM algorithm for emission tomography. In this re-derivation, the complete data explicitly enters the objective function as an unknown variable. While the entire complete data gets updated in each iteration of EM, in C-OSEM the complete data is updated only along ordered subsets. C-OSEM has a straightforward extension to the MAP case especially when using convex, smoothing priors. Unlike RAMLA and BSREM, C-OSEM does not require relaxation parameters to be set at each iteration. We derive the MAP C-OSEM algorithm using the separable surrogate method and anecdotally compare performance with MAP EM and BSREM.