# Complex-valued Federated Learning with Differential Privacy and MRI Applications

arXiv: https://arxiv.org/abs/2110.03478 · HTML: https://mlsanity.com/paper/2110.03478/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 30 references that are in the map.
- First posted on arXiv 7 Oct 2021.

## Builds on (most cited first, 11 of 11)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Adaptive Federated Optimization](https://mlsanity.com/paper/2003.00295/) (2020)
- [The Medical Segmentation Decathlon](https://mlsanity.com/paper/2106.05735/) (2021)
- [Weight Normalization: A Simple Reparameterization to Accelerate Training of Deep Neural Networks](https://mlsanity.com/paper/1602.07868/) (2016)
- [Flower: A Friendly Federated Learning Research Framework](https://mlsanity.com/paper/2007.14390/) (2020)
- [Deep Complex Networks](https://mlsanity.com/paper/1705.09792/) (2017)
- [Better than Real: Complex-valued Neural Nets for MRI Fingerprinting](https://mlsanity.com/paper/1707.00070/) (2017)
- [DeepMCAT: Large-Scale Deep Clustering for Medical Image Categorization](https://mlsanity.com/paper/2110.00109/) (2021)
- [Differential Privacy for Power Grid Obfuscation](https://mlsanity.com/paper/1901.06949/) (2019)
- [Deep Learning-based Type Identification of Volumetric MRI Sequences](https://mlsanity.com/paper/2106.03208/) (2021)

## Built on by (most cited first, 5 of 5)

- [Federated Learning of Generative Image Priors for MRI Reconstruction](https://mlsanity.com/paper/2202.04175/) (2022)
- [One Model to Unite Them All: Personalized Federated Learning of Multi-Contrast MRI Synthesis](https://mlsanity.com/paper/2207.06509/) (2022)
- [Differential privacy for medical deep learning: methods, tradeoffs, and deployment implications](https://mlsanity.com/paper/2506.00660/) (2025)
- [Federated nnU-Net for Privacy-Preserving Medical Image Segmentation](https://mlsanity.com/paper/2503.02549/) (2025)
- [Complex Network for Complex Problems: A comparative study of CNN and Complex-valued CNN](https://mlsanity.com/paper/2302.04584/) (2023)

## Abstract (arXiv)

Federated learning enhanced with Differential Privacy (DP) is a powerful privacy-preserving strategy to protect individuals sharing their sensitive data for processing in fields such as medicine and healthcare. Many medical applications, for example magnetic resonance imaging (MRI), rely on complex-valued signal processing techniques for data acquisition and analysis. However, the appropriate application of DP to complex-valued data is still underexplored. To address this issue, from the theoretical side, we introduce the complex-valued Gaussian mechanism, whose behaviour we characterise in terms of f-DP, (varepsilon, δ)-DP and R'enyi-DP. Moreover, we generalise the fundamental algorithm DP stochastic gradient descent to complex-valued neural networks and present novel complex-valued neural network primitives compatible with DP. Experimentally, we showcase a proof-of-concept by training federated complex-valued neural networks with DP on a real-world task (MRI pulse sequence classification in k-space), yielding excellent utility and privacy. Our results highlight the relevance of combining federated learning with robust privacy-preserving techniques in the MRI context.