EFFECT of PRIOR SMOOTHING on the CONVERGENCE of PROXIMAL ALGORITHMS for PET and SPECT RECONSTRUCTION

Proximal-based optimisation algorithms have been developed to be able to handle nondifferentiable functions. They have been widely studied for image reconstruction and denoising with priors such as the popular Total Variation (TV). Relatively little work has been done in evaluating their convergence performance with smooth priors that are more commonly used in emission tomography. We investigated the effect of varying the magnitude of a smoothing parameter for one image-based and one anatomical-based TV-like prior on the convergence rate of two proximal and two gradient-based algorithms for PET and SPECT reconstruction. The results suggest that the smoothness of a prior has less effect on the convergence rate for proximal algorithms than gradient-based algorithms. As expected, a smoother function results in faster convergence for gradient-based algorithms. A smoother function results in a slightly decreased convergence rate for proximal algorithms. Over-smoothing of the function resulted in under-regularisation and the breakdown of convergence observations.