Objective. Estimating the ongoing phase of oscillations in electroencephalography (EEG) recordings is an important aspect of understanding brain function, as well as for the development of phase-dependent closed-loop real-time systems that deliver stimuli. Such stimuli may take the form of direct brain stimulation (for example transcranial magnetic stimulation), or sensory stimuli (for example presentation of an auditory stimulus). We identify two linked problems related to estimating the phase of EEG rhythms with a specific focus on the alpha-band: 1) when the signal after a specific stimulus is unknown (real-time case), or 2) when it is corrupted by the presence of the stimulus itself (offline analysis). We propose methods to estimate the phase at the presentation time of these stimuli. Approach. Machine learning methods are used to learn the causal mapping from an unprocessed EEG recording to a phase estimate generated with a non-causal signal processing chain....

中文翻译：

---

实时应用中脑电节律的相位估计。

目的。估计脑电图（EEG）记录中正在进行的振荡阶段是理解脑功能的重要方面，也是开发可提供刺激的相位相关的闭环实时系统的重要方面。这样的刺激可以采取直接脑刺激（例如经颅磁刺激）或感觉刺激（例如听觉刺激的表现）的形式。我们确定了两个与估计脑电节律相位有关的相关问题，尤其是在阿尔法频段上：1）当特定刺激后的信号未知时（实时情况），或2）当信号被脑电波破坏时。刺激本身的存在（离线分析）。我们提出了在这些刺激的表现时估计相位的方法。方法。