  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 (NLEI), a self-supervised learning approach to eliminate the need for
ground truth for deep MRF image reconstruction. NLEI extends the recent
Equivariant Imaging framework to nonlinear inverse problems such as MRF. Only
fast, compressed-sampled MRF scans are used for training. NLEI 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 (self-supervised learning) closely approaches
the performance of supervised learning, despite not using ground truth during
training.
