An Ordered Subsets Algorithm for Transmission Tomography

The ordered subsets EM (OSEM) algorithm has enjoyed considerable interest for emission image reconstruction due to its acceleration of the original EM algorithm and ease of programming. The transmission EM reconstruction algorithm converges very slowly and is not used in practice, particularly because there are faster simultaneous update algorithms that converge much faster. We introduce such an algorithm called separable paraboloidal surrogates (SPS) in this paper which is also monotonic even with nonzero background counts. We demonstrate that the ordered subsets method can also be applied to the new algorithm to accelerate “convergence” for the transmission tomography problem, albeit with similar sacrifice of global convergence properties as OSEM. We implemented and evaluated this ordered subsets transmission (OSTR) algorithm. The results indicate that the OSTR algorithm speeds up the increase in the objective function by roughly the number of subsets in the early iterates when compared to the ordinary SPS algorithm. We compute mean square errors and segmentation errors for different methods and show that OSTR method is superior to OSEM applied to the logarithm of the transmission data. But, penalized-likelihood reconstructions yield the best quality images among all other methods tested.