脑电信号成分稀疏分析范式及其可行证明

Sparse Component Analysis Paradigm of EEG Signal and Its Feasibility

稀疏分解技术作为一种可靠的信号处理与传输方法,在包括EEG的多种时变信号分析和处理领域得到了广泛的应用。在EEG信号的成分分析中,现有算法(ICA,EMD)等都存在分解结果与真实成分显著不符的情况,难以对实际成分的波形进行估计。本文在稀疏分解算法基础上,通过对样本稀疏分布情况进行度量,给出了一个经过改良的稀疏性能评价指标(SPI)并以此建立了一个新的成分分析范式和相应的优化函数,经过理论和实际证明,该范式在成分分析领域能比传统方法更有效地使分解结果趋向于真实成分,对EEG信号、乃至其他时变信号的成分解析都具有相当的积极意义。

As a reliable signal processing and transmission method,sparse decomposition technology has been widely applied in many time-varying signal analysis and processing fields including EEG.Existing algorithms such as ICA and EMD often(almost always)bring significant discrepancy between their decomposition results and the real components,so it is difficult to estimate the waveform of the actual components by these algorithms.This paper provides an improved sparse performance index(SPI)by measuring the sparse distribution of the EEG samples,and introduces a new paradigm of component analysis and its optimizing function based on the sparse decomposition algorithm.We also prove by theory and practice that this paradigm can make the decomposition result tend to real components more effectively than traditional methods in the field of compositional analysis,which will provide considerable positive advantages to analysis of EEG and other time-varying signals.