Investigation of the preconditioner-parameter in the preconditioned Chambolle-Pock algorithm applied to optimization-based image reconstruction.

Abstract

The optimization-based image reconstruction methods have been thoroughly investigated in the field of medical imaging. The Chambolle-Pock (CP) algorithm may be employed to solve these convex optimization image reconstruction programs. The preconditioned CP (PCP) algorithm has been shown to have much higher convergence rate than the ordinary CP (OCP) algorithm. This algorithm utilizes a preconditioner-parameter to tune the implementation of the algorithm to the specific application, which ranges from 0 and 2, but is often set to 1. In this work, we investigated the impact of the preconditioner-parameter on the convergence rate of the PCP algorithm when it is applied to the TV constrained, data-divergence minimization (TVDM) optimization based image reconstruction. We performed the investigations in the context of 2D computed tomography (CT) and 3D electron paramagnetic resonance imaging (EPRI). For 2D CT, we used the Shepp-Logan and two FORBILD phantoms. For 3D EPRI, we used a simulated 6-spheres phantom and a physical phantom. Study results showed that the optimal preconditioner-parameter depends on the specific imaging conditions. Simply setting the parameter equal to 1 cannot guarantee a fast convergence rate. Thus, this study suggests that one should adaptively tune the preconditioner-parameter to obtain the optimal convergence rate of the PCP algorithm.