Complex-valued Federated Learning with Differential Privacy and MRI Applications

TL;DR

This paper introduces a complex-valued Gaussian mechanism for differential privacy, extends DP stochastic gradient descent to complex neural networks, and demonstrates effective privacy-preserving federated learning on MRI data.

Contribution

It develops the first theoretical framework for applying differential privacy to complex-valued data and neural networks, with practical validation on MRI applications.

Findings

Successful training of differentially private federated complex-valued neural networks on MRI data

The complex-valued Gaussian mechanism satisfies various differential privacy definitions

Demonstrates high utility and privacy in MRI pulse sequence classification

Abstract

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, $(\varepsilon, \delta)$-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.