On the Characterization and Reduction of Ill-Conditioning in Jointly Estimating Proton Density, T2* Decay and the Field Map

Abstract

We employ principal angles as a tool to demonstrate that the complex frequency is the main cause for ill-conditioning of model-based MRI reconstruction. We show that kernels of EPI and spiral trajectories have different null sets that can be utilized to improve the conditioning. This idea is further verified based on synthesized phantom data.