通过小波变换与噪声优化，提升隐私保护下的联邦学习模型性能。

Federated learning has emerged as an attractive approach to protect data privacy by eliminating the need for sharing clients' data while reducing communication costs compared with centralized machine learning algorithms. However, recent studies have shown that federated learning alone does not guarantee privacy, as private data may still be inferred from the uploaded parameters to the central server. In order to successfully avoid data leakage, adopting differential privacy (DP) in the local optimization process or in the local update aggregation process has emerged as two feasible ways for achieving sample-level or user-level privacy guarantees respectively, in federated learning models. However, compared to their non-private equivalents, these approaches suffer from a poor utility. To improve the privacy-utility trade-off, we present a modification to these vanilla differentially private algorithms based on a Haar wavelet transformation step and a novel noise injection scheme that significantly lowers the asymptotic bound of the noise variance. We also present a holistic convergence analysis of our proposed algorithm, showing that our method yields better convergence performance than the vanilla DP algorithms. Numerical experiments on real-world datasets demonstrate that our method outperforms existing approaches in model utility while maintaining the same privacy guarantees.