Background and objective

There are many phenomena that lead to changes in the power spectrum of a given signal, and their detection has been a challenge that has received considerable attention over the years. Objective Response Detection (ORD) techniques are a set of tools that perform automated tests for such a task, allowing thus to automatically track changes in the spectrum. The performance of these detectors is affected by the signal-to-noise ratio (SNR) of the recorded signal as well as the length of the available data. The Global F Test (GFT) is a promising detector that can be used to test whether there is a statistically significant difference between the spectrum before and during an event. In fact, this detector has proved useful in the detection of event-related desynchronization/synchronization (ERD/ERS), where only amplitude, but not the phase, changes are locked to the stimulus. In order to improve the statistical power of the GFT (for the same length of recording), multiple channels recorded simultaneously can be included. This concept is called Multivariate Response Detection. The aim of the current work is to extend the GFT to the multivariate (multichannel) case.

Methods

Firstly, the single channel normalization of the GFT is presented as a new ORD detector - the global Beta test (GBT). After that, three multivariate extensions of this new test are derived. The critical values used in the detection of spectral changes are obtained by using theoretical distributions, and where this is intractable, by means of Monte Carlo simulations. The probability of detection (PD) of each technique was estimated using simulation and was used in order to compare the detectors performance. A practical example with the electroencephalogram (EEG) from 10 volunteers under intermittent photic stimulation was also provided.

Results

The statistics under both the null and alternative hypothesis could be obtained for all detectors. Simulated results for PD demonstrate the strong potential of the proposed method and the performances in EEG data are always improved with increasing number of signals.

Conclusion

If more than one signal is available, then the multivariate extensions may provide significant benefit compared to the original GFT.

中文翻译：

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针对信号中隐藏的周期性及其对多元系统的扩展的全局Beta测试。

背景和目标

有许多现象会导致给定信号的功率谱发生变化，多年来，对它们的检测一直是一项备受关注的挑战。客观响应检测（ORD）技术是为此类任务执行自动测试的一组工具，从而可以自动跟踪光谱的变化。这些检测器的性能受记录信号的信噪比（SNR）以及可用数据长度的影响。全局F检验（GFT）是一种很有前途的检测器，可用于检测事件发生之前和发生期间频谱之间是否存在统计上显着的差异。实际上，该检测器已被证明可用于检测与事件相关的失步/同步（ERD / ERS），其中仅幅度而不是相位，变化被锁定在刺激因素上。为了提高GFT的统计能力（对于相同记录长度），可以包括同时记录的多个通道。这个概念称为多变量响应检测。当前工作的目的是将GFT扩展到多变量（多通道）情况。

方法

首先，将GFT的单通道归一化作为新的ORD检测器-全局Beta测试（GBT）提出。之后，得出了这个新测试的三个多元扩展。通过使用理论分布获得光谱变化检测中使用的临界值，并且在难以解决的情况下可以通过蒙特卡洛模拟获得。使用模拟估算了每种技术的检测概率（PD），并将其用于比较检测器的性能。还提供了一个来自10名志愿者在间歇性光刺激下的脑电图（EEG）的实例。

结果

可以针对所有检测器获得零假设和替代假设下的统计信息。PD的仿真结果证明了该方法的强大潜力，并且随着信号数量的增加，EEG数据的性能始终得到改善。

结论

如果有多个信号可用，则与原始GFT相比，多变量扩展可能会带来明显的好处。