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基于循环节律连接随机过程向量的脑机接口中的高级建模与信号处理方法。

Advanced Modeling and Signal Processing Methods in Brain-Computer Interfaces Based on a Vector of Cyclic Rhythmically Connected Random Processes.

机构信息

Faculty of Electrical Engineering, Automatic Control and Informatics, Opole University of Technology, 45-758 Opole, Poland.

Institute of Telecommunications and Global Information Space, National Academy of Sciences of Ukraine, 02000 Kyiv, Ukraine.

出版信息

Sensors (Basel). 2023 Jan 9;23(2):760. doi: 10.3390/s23020760.

DOI:10.3390/s23020760
PMID:36679557
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC9866141/
Abstract

In this study is substantiated the new mathematical model of vector of electroencephalographic signals, registered under the conditions of multiple repetitions of the mental control influences of brain-computer interface operator, in the form of a vector of cyclic rhythmically connected random processes, which, due to taking into account the stochasticity and cyclicity, the variability and commonality of the rhythm of the investigated signals have a number of advantages over the known models. This new model opens the way for the study of multidimensional distribution functions; initial, central, and mixed moment functions of higher order such as for each electroencephalographic signal separately; as well as for their respective compatible probabilistic characteristics, among which the most informative characteristics can be selected. This provides an increase in accuracy in the detection (classification) of mental control influences of the brain-computer interface operators. Based on the developed mathematical model, the statistical processing methods of vector of electroencephalographic signals are substantiated, which consist of statistical evaluation of its probabilistic characteristics and make it possible to conduct an effective joint statistical estimation of the probability characteristics of electroencephalographic signals. This provides the basis for coordinated integration of information from different sensors. The use of moment functions of higher order and their spectral images in the frequency domain, as informative characteristics in brain-computer interface systems, are substantiated. Their significant sensitivity to the mental controlling influence of the brain-computer interface operator is experimentally established. The application of Bessel's inequality to the problems of reducing the dimensions (from 500 to 20 numbers) of the vectors of informative features makes it possible to significantly reduce the computational complexity of the algorithms for the functioning of brain-computer interface systems. Namely, we experimentally established that only the first 20 values of the Fourier transform of the estimation of moment functions of higher-order electroencephalographic signals are sufficient to form the vector of informative features in brain-computer interface systems, because these spectral components make up at least 95% of the total energy of the corresponding statistical estimate of the moment functions of higher-order electroencephalographic signals.

摘要

在这项研究中，证实了一种新的脑机接口操作员心理控制影响的脑电图信号向量的数学模型，其形式为循环节律连接的随机过程向量，由于考虑到随机性和周期性，该信号的可变性和共性具有优于已知模型的一些优势。这个新模型为研究多维分布函数开辟了道路；对每个脑电图信号分别进行初始、中心和更高阶混合矩函数的研究；以及它们各自的相容概率特征，其中可以选择最具信息量的特征。这提高了检测（分类）脑机接口操作员心理控制影响的准确性。基于所开发的数学模型，证实了脑电图信号向量的统计处理方法，该方法包括对其概率特征进行统计评估，从而可以对脑电图信号的概率特征进行有效的联合统计估计。这为来自不同传感器的信息的协调集成提供了基础。在脑机接口系统中，使用高阶矩函数及其频域的谱图像作为信息特征是合理的。实验证明它们对脑机接口操作员的心理控制影响具有显著的敏感性。贝塞尔不等式在降低信息特征向量的维数（从 500 维减少到 20 维）问题中的应用使得脑机接口系统的算法的计算复杂度大大降低。即，我们实验证明，仅使用高阶脑电图信号矩函数估计的傅里叶变换的前 20 个值就足以在脑机接口系统中形成信息特征向量，因为这些谱分量至少构成了相应的高阶脑电图信号矩函数统计估计的总能量的 95%。

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