EEG-CPDD: A Covariance-Preserving Diffusion Denoiser for Reliable EEG Source Localization

Electroencephalographic (EEG) source localization (ESL) is highly sensitive to noise. Although deep learning-based denoising methods can suppress artifacts, their mean squared error (MSE)-driven optimization tends to induce over-smoothing, which distorts signal covariance and thus degrades source reconstruction. To address this limitation, we propose EEG-CPDD, a covariance-preserving denoising framework based on conditional diffusion probabilistic models. Unlike conventional approaches, EEG-CPDD performs probabilistic signal reconstruction guided by noise information rather than learning pointwise conditional expectations. Specifically, we design a noise prediction network termed RLinDenoiseNet, which integrates three key modules: RLinFormer captures long-range artifact dependencies via low-rank attention, FFiLM injects frequency-domain noise-level information to calibrate denoising strength, and SEFuse fuses dual-stream features through channel-wise attention. Extensive experiments on multiple benchmark datasets demonstrate that EEG-CPDD achieves superior denoising performance while faithfully preserving the spatial covariance structure. Moreover, systematic evaluations across various source localization algorithms show that EEG-CPDD consistently reduces dipole localization error, improves energy reconstruction fidelity, and enhances robustness against parameter selection, confirming that covariance-preserving denoising provides a practical and reliable preprocessing foundation for ESL.