Under-relaxed quasi-Newton acceleration for an inverse fixed-point problem coming from Positron Emission Tomography

Abstract

Abstract Quasi-Newton acceleration is an interesting tool to improve the performance of numerical methods based on the fixed-point paradigm. In this paper, a briefly description of the compartmental model employed for a typical task in perfusion imaging is presented. Next, a quasi-Newton strategy for accelerating the convergence of fixed-point iterations is analyzed. For that, classical secant updates are considered. Finally, the quasi-Newton strategy is applied on the practical problem of represent the kinetic behavior of a PET (Positron Emission Tomography) tracer during cardiac perfusion. The performance of the method when applied to real data problems is illustrated numerically.