# Geometry of Deep Learning for Magnetic Resonance Fingerprinting

arXiv: https://arxiv.org/abs/1809.01749 · HTML: https://mlsanity.com/paper/1809.01749/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Sep 2018.

## Built on by (most cited first, 7 of 7)

- [Cram'er-Rao bound-informed training of neural networks for quantitative MRI](https://mlsanity.com/paper/2109.10535/) (2021)
- [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)
- [Solving inverse problems with deep neural networks driven by sparse signal decomposition in a physics-based dictionary](https://mlsanity.com/paper/2107.10657/) (2021)
- [Adaptive Gate-Aware Mamba Networks for Magnetic Resonance Fingerprinting](https://mlsanity.com/paper/2507.03369/) (2025)
- [MRI2Qmap: multi-parametric quantitative mapping with MRI-driven denoising priors](https://mlsanity.com/paper/2603.11316/) (2026)
- [DeepPV-MRF: End-to-End Partial-Volume Fraction Estimation from MR Fingerprinting Time Series](https://mlsanity.com/paper/2610.19894/) (2026)

## Abstract (arXiv)

Current popular methods for Magnetic Resonance Fingerprint (MRF) recovery are bottlenecked by the heavy storage and computation requirements of a dictionary-matching (DM) step due to the growing size and complexity of the fingerprint dictionaries in multi-parametric quantitative MRI applications. In this paper we study a deep learning approach to address these shortcomings. Coupled with a dimensionality reduction first layer, the proposed MRF-Net is able to reconstruct quantitative maps by saving more than 60 times in memory and computations required for a DM baseline. Fine-grid manifold enumeration i.e. the MRF dictionary is only used for training the network and not during image reconstruction. We show that the MRF-Net provides a piece-wise affine approximation to the Bloch response manifold projection and that rather than memorizing the dictionary, the network efficiently clusters this manifold and learns a set of hierarchical matched-filters for affine regression of the NMR characteristics in each segment.