# Better than Real: Complex-valued Neural Nets for MRI Fingerprinting

arXiv: https://arxiv.org/abs/1707.00070 · HTML: https://mlsanity.com/paper/1707.00070/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jul 2017.

## Built on by (most cited first, 30 of 30)

- [A Survey of Complex-Valued Neural Networks](https://mlsanity.com/paper/2101.12249/) (2021)
- [Physics-Driven Deep Learning for Computational Magnetic Resonance Imaging](https://mlsanity.com/paper/2203.12215/) (2022)
- [How important are activation functions in regression and classification? A survey, performance comparison, and future directions](https://mlsanity.com/paper/2209.02681/) (2022)
- [Building Blocks for a Complex-Valued Transformer Architecture](https://mlsanity.com/paper/2306.09827/) (2023)
- [Theory and Implementation of Complex-Valued Neural Networks](https://mlsanity.com/paper/2302.08286/) (2023)
- [Towards Understanding Theoretical Advantages of Complex-Reaction Networks](https://mlsanity.com/paper/2108.06711/) (2021)
- [Quantitative approximation results for complex-valued neural networks](https://mlsanity.com/paper/2102.13092/) (2021)
- [Complex-valued Federated Learning with Differential Privacy and MRI Applications](https://mlsanity.com/paper/2110.03478/) (2021)
- [Deep, Deep Learning with BART](https://mlsanity.com/paper/2202.14005/) (2022)
- [Cram'er-Rao bound-informed training of neural networks for quantitative MRI](https://mlsanity.com/paper/2109.10535/) (2021)
- [Co-domain Symmetry for Complex-Valued Deep Learning](https://mlsanity.com/paper/2112.01525/) (2021)
- [Universal approximation with complex-valued deep narrow neural networks](https://mlsanity.com/paper/2305.16910/) (2023)
- [Qualitative neural network approximation over R and C: Elementary proofs for analytic and polynomial activation](https://mlsanity.com/paper/2203.13410/) (2022)
- [Complex-Valued Neural Networks for Data-Driven Signal Processing and Signal Understanding](https://mlsanity.com/paper/2309.07948/) (2023)
- [Complex-valued Neural Networks -- Theory and Analysis](https://mlsanity.com/paper/2312.06087/) (2023)
- [Steinmetz Neural Networks for Complex-Valued Data](https://mlsanity.com/paper/2409.10075/) (2024)
- [Deep Sequence Modeling with Quantum Dynamics: Language as a Wave Function](https://mlsanity.com/paper/2602.22255/) (2026)
- [Improving Quaternion Neural Networks with Quaternionic Activation Functions](https://mlsanity.com/paper/2406.16481/) (2024)
- [Towards White-Box Deep Wireless Sensing](https://mlsanity.com/paper/2507.21799/) (2025)
- [RotaTouille: Rotation Equivariant Deep Learning for Contours](https://mlsanity.com/paper/2508.16359/) (2025)
- [When do complex-valued neural networks help? A study of representation, geometry, and optimization](https://mlsanity.com/paper/2605.27673/) (2026)
- [Syntax-Aware Complex-Valued Neural Machine Translation](https://mlsanity.com/paper/2307.08586/) (2023)
- [Emerging Approaches for THz Array Imaging: A Tutorial Review and Software Tool](https://mlsanity.com/paper/2309.08844/) (2023)
- [Generalized Activation via Multivariate Projection](https://mlsanity.com/paper/2309.17194/) (2023)
- [Quantitative perfusion maps using a novelty spatiotemporal convolutional neural network](https://mlsanity.com/paper/2312.05279/) (2023)
- [I Can't Believe It's Not Real: CV-MuSeNet: Complex-Valued Multi-Signal Segmentation](https://mlsanity.com/paper/2506.11048/) (2025)
- [Phase-Aware Deep Learning with Complex-Valued CNNs for Audio Signal Applications](https://mlsanity.com/paper/2510.09926/) (2025)
- [Perturbing the Phase: Analyzing Adversarial Robustness of Complex-Valued Neural Networks](https://mlsanity.com/paper/2602.06577/) (2026)
- [Exploring Polarimetric Properties Preservation during Reconstruction of PolSAR images using Complex-valued Convolutional Neural Networks](https://mlsanity.com/paper/2602.07094/) (2026)
- [Complex-Valued Unitary Representations as Classification Heads for Improved Uncertainty Quantification in Deep Neural Networks](https://mlsanity.com/paper/2602.15283/) (2026)

## Abstract (arXiv)

The task of MRI fingerprinting is to identify tissue parameters from complex-valued MRI signals. The prevalent approach is dictionary based, where a test MRI signal is compared to stored MRI signals with known tissue parameters and the most similar signals and tissue parameters retrieved. Such an approach does not scale with the number of parameters and is rather slow when the tissue parameter space is large. Our first novel contribution is to use deep learning as an efficient nonlinear inverse mapping approach. We generate synthetic (tissue, MRI) data from an MRI simulator, and use them to train a deep net to map the MRI signal to the tissue parameters directly. Our second novel contribution is to develop a complex-valued neural network with new cardioid activation functions. Our results demonstrate that complex-valued neural nets could be much more accurate than real-valued neural nets at complex-valued MRI fingerprinting.