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

arXiv: https://arxiv.org/abs/2211.12786 · HTML: https://mlsanity.com/paper/2211.12786/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 14 references that are in the map.
- First posted on arXiv 23 Nov 2022.

## Builds on (most cited first, 6 of 6)

- [Equivariant Imaging: Learning Beyond the Range Space](https://mlsanity.com/paper/2103.14756/) (2021)
- [Robust Equivariant Imaging: a fully unsupervised framework for learning to image from noisy and partial measurements](https://mlsanity.com/paper/2111.12855/) (2021)
- [Compressive MR Fingerprinting reconstruction with Neural Proximal Gradient iterations](https://mlsanity.com/paper/2006.15271/) (2020)
- [A Plug-and-Play Approach to Multiparametric Quantitative MRI: Image Reconstruction using Pre-Trained Deep Denoisers](https://mlsanity.com/paper/2202.05269/) (2022)
- [Multi-shot Echo Planar Imaging for accelerated Cartesian MR Fingerprinting: an alternative to conventional spiral MR Fingerprinting](https://mlsanity.com/paper/1906.08195/) (2019)
- [Accurate parameter estimation using scan-specific unsupervised deep learning for relaxometry and MR fingerprinting](https://mlsanity.com/paper/2112.03815/) (2021)

## Built on by (most cited first, 3 of 3)

- [Scale-Equivariant Imaging: Self-Supervised Learning for Image Super-Resolution and Deblurring](https://mlsanity.com/paper/2312.11232/) (2023)
- [Denoising Diffusion Probabilistic Models for Magnetic Resonance Fingerprinting](https://mlsanity.com/paper/2410.23318/) (2024)
- [Deep Image Priors for Magnetic Resonance Fingerprinting with pretrained Bloch-consistent denoising autoencoders](https://mlsanity.com/paper/2407.19866/) (2024)

## Abstract (arXiv)

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.