AI 中文总结
研究旨在从生物信号记录中估计事件锁定模板，基于斯坦无偏风险估计开发数据驱动框架，联合优化正则化结构及其幅度，通过将正则化算子参数化为卷积核学习惩罚结构，扩展SURE到有色噪声，跨模态验证显示相比其他方法增益明显。
AI 中文摘要
通过正则化最小二乘法从生物信号记录中估计事件锁定模板需要选择正则化结构及其幅度，通常是凭经验进行选择。我们基于斯坦无偏风险估计（SURE）开发了一个数据驱动框架来联合优化这两者。通过将正则化算子参数化为卷积核，该方法直接从数据中学习惩罚结构，以一种固定差分算子缩放无法实现的方式将平滑性增强与岭状收缩相结合。虽然标准SURE假设为白噪声，但生物信号噪声具有时间自相关性，因此我们通过基于噪声协方差矩阵的结构化校正替换其标量迹项，将SURE扩展到有色噪声。对于AR(1)噪声，这种校正仅需要两个参数，即噪声方差和滞后1自相关性，两者均可从事件前基线估计。在听觉事件相关电位、P300脑机接口数据和心电图形态上的跨模态验证表明，与替代方法相比有一致的增益，所有这些都是在每个类别$K = 5$个事件的情况下——这是与快速校准和个性化最相关的情况。
英文摘要
Estimating event-locked templates from bio-signal recordings via regularized least-squares requires choosing both the regularization structure and its magnitude, choices that are typically made heuristically. We develop a data-driven framework based on Stein's Unbiased Risk Estimate (SURE) that jointly optimizes both. By parameterizing the regularization operator as a convolution kernel, our method learns the penalty structure directly from the data, combining smoothness enforcement with ridge-like shrinkage in a way that cannot be achieved by scaling a fixed difference operator. While standard SURE assumes white noise, biosignal noise exhibits temporal autocorrelation. We therefore extend SURE to colored noise by replacing its scalar trace term with a structured correction based on the noise covariance matrix. For AR(1) noise, this correction requires only two parameters, the noise variance and the lag-1 autocorrelation, both estimable from pre-event baselines. Cross-modality validation on auditory event-related potentials, P300 brain--computer interface data, and ECG morphology demonstrates consistent gains compared to alternative methods, all at $K=5$ events per class - the regime most relevant for rapid calibration and personalization.
