Unimodality and Radial Monotonicity of the Magnetic Resonance Fingerprinting T1/T2 Matching Objective

Abstract: Magnetic resonance fingerprinting (MRF) estimates tissue parameters by matching an acquired MR signal time course to entries in a Bloch- or EPG-simulated dictionary. However, no study has yet proven the uniqueness of the matching results. In two earlier studies by exhaustive objective mapping I showed that for two widely used MRF sequences the normalized-correlation objective exhibits a single dominant peak at the true T1/T2 values and decreases smoothly away from that peak. These empirical properties motivated the fast MRF-ZOOM search algorithm even without using a pre-generated signal dictionary, but their theoretical basis has remained incomplete. The purpose of this work is to develop a mathematical framework for the MRF matching objective under normalized-correlation matching.