Comparison of numerical convergence speeds of convergent and accelerated algorithms for penalized likelihood PET image

Computational cost is a major challenge for 3D PET image reconstruction. Traditional ordered subsets based methods, such as OS-EM, accelerate the reconstruction process but in general are not convergent. In recent years, accelerated and convergent algorithms have been developed for PET image reconstruction. In this work, we study the numerical convergence speeds for three types of ordered subsets based convergent algorithms for penalized likelihood image reconstruction: BSREM, COSEM, and OS-MAP. The study of the computational cost for these algorithms is important in guiding numerical algorithm selection in clinical applications of penalized likelihood image reconstruction. A special case of the q-generalized Gaussian Markov random field (q-GGMRF) was used as the prior and a separable surrogate function for the prior was derived for COSEM and OS-MAP. The experiments were performed with simulated data obtained from a resolution phantom and the NCAT phantom as well as with clinical data containing inserted lesions. We investigated the local convergence in lesion activity recovery and the global convergence in the objective function as a function of iteration number. The experiments indicate that BSREM achieves faster convergence with a good selection of relaxation parameters compared to COSEM. OS-MAP's convergence speed with a good rule for gradually reducing the number of subsets to one was comparable to that of BSREM.