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

TL;DR

This paper introduces NLEI, a self-supervised deep learning method for quantitative MRI reconstruction that eliminates the need for ground truth data by leveraging geometric invariances and a neural network-approximated Bloch response model.

Contribution

NLEI extends equivariant imaging to nonlinear inverse problems, enabling high-quality tissue mapping from compressed MRI scans without ground truth data.

Findings

NLEI achieves performance close to supervised methods.

It effectively learns tissue mapping using spatiotemporal priors.

Retrospective tests show strong results across different acquisition settings.

Abstract

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.