Fast hybrid algorithms for PET image reconstruction

We describe a hybrid approach to iterative PET image reconstruction in which we combine three algorithms: preconditioned conjugate gradient (PCG), ordered subsets separable paraboloidal surrogate (OSSPS), and emission reconstruction incremental optimization transfer (ERIOT). These algorithms exhibit quite different convergence behavior, e.g. the initial convergence of OSSPS is fast but it soon enters a limit cycle. Conversely, initial convergence of PCG is slow compared to OSSPS and ERIOT but its asymptotic behavior is the fastest. The hybrid approach estimates convergence behavior for each method by fitting an exponential to the objective function as a function of iteration number and switches between the algorithms to optimize the convergence behavior throughout the iterations. This hybrid approach is compared to each of the component algorithms in application to simulated PET data demonstrating a reduction of at least 50% in iterations required for effective convergence compared to use of PCG alone.