Despite recent progress in enhancing the privacy of federated learning (FL) via differential privacy (DP), the trade-off of DP between privacy protection and performance is still underexplored for real-world medical scenario. In this paper, we propose to optimize the trade-off under the context of client-level DP, which focuses on privacy during communications. However, FL for medical imaging involves typically much fewer participants (hospitals) than other domains (e.g., mobile devices), thus ensuring clients be differentially private is much more challenging. To tackle this problem, we propose an adaptive intermediary strategy to improve performance without harming privacy. Specifically, we theoretically find splitting clients into sub-clients, which serve as intermediaries between hospitals and the server, can mitigate the noises introduced by DP without harming privacy. Our proposed approach is empirically evaluated on both classification and segmentation tasks using two public datasets, and its effectiveness is demonstrated with significant performance improvements and comprehensive analytical studies. Code is available at: https://github.com/med-air/Client-DP-FL.
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