The ordered subsets mirror descent optimization method with applications to tomography

We describe an optimization problem arising in reconstructing three-dimensi onal medical images from positron emission tomography (PET). A mathematical model of the problem, based on the maximum likelihood principle, is posed as a problem of minimizing a convex function of several million variables o ver the standard simplex. To solve a problem of these characteristics, we d evelop and implement a new algorithm, ordered subsets mirror descent, and d emonstrate, theoretically and computationally, that it is well suited for s olving the PET reconstruction problem.