Globally Convergent Ordered Subsets Algorithms: Application to Tomography

We present new algorithms for penalized-likelihood image reconstruction: modified BSREM (block sequential regularized expectation maximization) and relaxed OS-SPS (ordered subsets separable paraboloidal surrogates). Both of them are globally convergent to the unique solution, easily incorporate convex penalty functions, and are parallelizable—updating all voxels (or pixels) simultaneously. They belong to a class of relaxed ordered subsets algorithms. We modify the scaling function of the existing BSREM (De Pierro and Yamagishi, 01) so that we can prove global convergence without previously imposed assumptions. We also introduce a diminishing relaxation parameter into the existing OS-SPS (Erdoğan and Fessler, 99) to achieve global convergence. We also modify the penalized-likelihood function to enable the algorithms to cover a zerobackground-event case. Simulation results show that the algorithms are both globally convergent and fast.