This paper introduces the FFT-Enhanced Kalman Filter (FFTKF), a differentially private optimization method that addresses the challenge of preserving performance in DP-SGD, where added noise typically degrades model utility. FFTKF integrates frequency-domain noise shaping with Kalman filtering to enhance gradient quality while preserving $(\varepsilon, \delta)$-DP guarantees. It employs a high-frequency shaping mask in the Fourier domain to concentrate differential privacy noise in less informative spectral components, preserving low-frequency gradient signals. A scalar-gain Kalman filter with finite-difference Hessian approximation further refines the denoised gradients. With a per-iteration complexity of $\mathcal{O}(d \log d)$, FFTKF demonstrates improved test accuracy over DP-SGD and DiSK across MNIST, CIFAR-10, CIFAR-100, and Tiny-ImageNet datasets using CNNs, Wide ResNets, and Vision Transformers. Theoretical analysis confirms that FFTKF maintains equivalent privacy guarantees while achieving a tighter privacy-utility trade-off through reduced noise and controlled bias.

本文提出了一种名为FFT增强卡尔曼滤波器（FFTKF）的差分隐私优化方法，旨在解决DP-SGD中添加噪声导致模型效用下降的挑战。FFTKF通过频域噪声塑形结合卡尔曼滤波，实现了梯度质量的提升，同时保持了(ε, δ)-差分隐私保证，显著提高了测试准确性。

基于谱和时间的差分隐私优化去噪