Cloud–edge collaborative intelligence for privacy-preserving electrical impedance tomography reconstruction with federated deep D-bar

Electrical impedance tomography (EIT) requires solving a nonlinear and severely ill-posed inverse problem from boundary current–voltage measurements. The D-bar method provides fast and stable direct reconstructions, but its low-pass regularization can blur object boundaries and limit spatial resolution. We propose HAFDD, a heterogeneity-aware federated deep D-bar framework that combines physics-based D-bar reconstruction with federated U-Net refinement across heterogeneous clients in a distributed cloud–edge environment. The framework enables collaborative intelligence across decentralized clients while keeping raw EIT measurements local and aggregating model updates under heterogeneous client distributions. All clients share acquisition-compatible configurations; the framework addresses statistical heterogeneity (non-IID data distributions) rather than structural heterogeneity (incompatible hardware or measurement protocols). Extensive experiments on simulated KIT4-style datasets compare HAFDD with classical, variational, centralized learning, and distributed learning baselines. On the in-distribution test set, HAFDD achieves a relative L1 error of 0.033 ± 0.02, a relative squared L2 error of 0.011 ± 0.01, and a Dice Score of 0.837 ± 0.08. Under out-of-distribution (OOD) testing, it maintains low reconstruction errors of 0.037 ± 0.01 and 0.012 ± 0.00, respectively, with a Dice Score of 0.839 ± 0.08 and a dynamic-range ratio of 0.965 ± 0.09. Compared with Local-Only, FedAvg, and FedProx, HAFDD substantially reduces reconstruction errors under distribution shift while maintaining competitive structural accuracy. These results show that heterogeneity-aware federated learning improves distributed AI robustness while preserving measurement-data decentralization across the cloud–edge continuum.