In EEG data acquired in the presence of fMRI, gradient-related spike artifacts contaminate the signal following the common preprocessing step of average artifact subtraction. Spike artifacts compromise EEG data quality since they overlap with the EEG signal in frequency, thereby confounding frequency-based inferences on activity. As well, spike artifacts can inflate or deflate correlations among time series, thereby confounding inferences on functional connectivity. We present Schrödinger filtering, which uses the Schrödinger equation to decompose the spike-containing input. The basis functions of the decomposition are localized and pulse-shaped, and selectively capture the various input peaks, with the spike components clustered at the beginning of the spectrum. Schrödinger filtering automatically subtracts the spike components from the data. On real and simulated data, we show that Schrödinger filtering (1) simultaneously accomplishes high spike removal and high signal preservation without affecting evoked activity, and (2) reduces spurious pairwise correlations in spontaneous activity. In these regards, Schrödinger filtering was significantly better than three other despiking techniques: median filtering, amplitude thresholding, and wavelet denoising. These results encourage the use of Schrödinger filtering in future EEG-fMRI pipelines, as well as in other spike-related applications (e.g., fMRI motion artifact removal or action potential extraction).

中文翻译：

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薛定谔滤波：一种用于 EEG-fMRI 梯度伪影的精确 EEG 去尖峰技术

在 fMRI 存在的情况下获得的 EEG 数据中，梯度相关的尖峰伪影会在平均伪影减法的常见预处理步骤之后污染信号。尖峰伪影会影响 EEG 数据质量，因为它们在频率上与 EEG 信号重叠，从而混淆了基于频率的活动推断。同样，尖峰伪影可以增加或减少时间序列之间的相关性，从而混淆对功能连接的推断。我们提出了薛定谔过滤，它使用薛定谔方程来分解包含尖峰的输入。分解的基函数是局部的和脉冲形状的，并有选择地捕获各种输入峰值，尖峰分量聚集在谱的开头。薛定谔过滤会自动从数据中减去尖峰成分。在真实和模拟数据上，我们表明薛定谔滤波 (1) 在不影响诱发活动的情况下同时实现了高尖峰消除和高信号保留，并且 (2) 减少了自发活动中的虚假成对相关性。在这些方面，薛定谔滤波明显优于其他三种去尖峰技术：中值滤波、幅度阈值和小波去噪。这些结果鼓励在未来的 EEG-fMRI 管道以及其他与尖峰相关的应用（例如，fMRI 运动伪影去除或动作电位提取）中使用薛定谔滤波。(2) 减少自发活动中的虚假成对相关性。在这些方面，薛定谔滤波明显优于其他三种去尖峰技术：中值滤波、幅度阈值和小波去噪。这些结果鼓励在未来的 EEG-fMRI 管道以及其他与尖峰相关的应用（例如，fMRI 运动伪影去除或动作电位提取）中使用薛定谔滤波。(2) 减少自发活动中的虚假成对相关性。在这些方面，薛定谔滤波明显优于其他三种去尖峰技术：中值滤波、幅度阈值和小波去噪。这些结果鼓励在未来的 EEG-fMRI 管道以及其他与尖峰相关的应用（例如，fMRI 运动伪影去除或动作电位提取）中使用薛定谔滤波。