Quantitative T1 mapping in the liver is an emerging biomarker of hepatic fibrosis and characterization of liver function. Existing T1 mapping methods in abdomen are generally sensitive to tissue fat and B1 inhomogeneities , both of which confound estimates of T1. Further, Cartesian methods may suffer from motion related ghosting artifacts. In this work, we propose to combine 3D-radial inversion recovery with chemical shift encoded imaging to jointly estimate T1 of water, T1 of fat, proton density fat fraction (PDFF), and B0 and B1 inhomogeneities. The feasibility and performance of the proposed method are evaluated with simulations, and phantom experiments.