Nonlinear Equivariant Imaging: Learning Multi-Parametric Tissue Mapping without Ground Truth for Compressive Quantitative MRI

Current state-of-the-art reconstruction for quantitative tissue maps from fast, compressive, Magnetic Resonance Fingerprinting (MRF), use supervised deep learning, with the drawback of requiring high-fidelity ground truth tissue map training data which is limited. This paper proposes NonLinear Equivariant Imaging for MRF (NLEIMRF), a self-supervised learning approach to eliminate the need for ground truth for deep MRF image reconstruction. NLEI-MRF extends the recent Equivariant Imaging framework to the MRF nonlinear inverse problem. Only compressed-sampled MRF scans are used for training. NLEI-MRF learns tissue mapping using spatiotemporal priors: spatial priors are obtained from the invariance of MRF data to a group of geometric image transformations, while temporal priors are obtained from a nonlinear Bloch response model approximated by a pre-trained neural network. Tested retrospectively on two acquisition settings, we observe that NLEI-MRF closely approaches the performance of supervised learning.