生理信号的欠定联合盲源分离研究

Joint Blind Source Separation (JBSS), aiming to analyze the target signal from multi-view/multi-modality simultaneously, is an effective way to analyze physiological signals. However, currently available JBSS methods always assume the number of sources is smaller than or equal to that of observations (overdetermined/determined). With the development of miniaturization technologies, especially in the field of mobile health monitoring, it is desirable to collect physiological signals using fewer sensors. It is difficult to satisfy these assumptions and the performance is deteriorated in such cases. In this project, we aim to explore the frontiers research topic of underdetermined JBSS and validate the proposed strategy via evaluating its performance on two typical kinds of physiological signals, including electroencephalography and speech signals. Based on time-frequency analysis and ensemble clustering, the number of sources is estimated accurately first. Then, considering the limited observations and the dependence information across datasets, we plan to jointly estimate the mixing matrices as well as the sources based on joint tensor canonical polyadic decomposition and expectation maximization algorithm. In addition, to enhance the practicability and the efficiency, we propose to employ the stochastic resonance and regularized nonlinear acceleration. The theory of blind source separation will be improved after the completion of this study. Moreover, it is of great importance for further research on physiological signal processing in the design of mobile health monitoring systems.

联合盲源分离对信号进行多视角或多模态地分析，是生理信号处理中的重要手段。然而，随着设备的小型化，现有联合盲源分离算法关于源信号数目少于或等于观测信号数目（超定或正定）的假设很难满足，影响了信号恢复的准确性。因此，亟需提出欠定联合盲源分离算法。项目拟对欠定联合盲源分离这一新兴前沿研究方向开展探索，并使用脑电、语音两类典型生理信号对研究方案进行验证。拟研究内容包括：1）针对源信号数目未知的问题，基于时频域分析和聚类集成，探索源信号数目估计方法；2）针对观测信号通道不足且数据集间存在关联的盲源分离问题，综合考虑欠定性和关联性，探索联合估计混合矩阵和恢复源信号的算法；3）为提升算法的实用性和时效性，基于随机共振和正则化非线性加速，研究辅助性噪声的添加方式和算法性能优化。相关成果可进一步完善盲源分离理论，并有望在移动健康监护系统的设计中取得具体应用，对研究其中的生理信号处理具有重要意义。

盲源分离旨在将无法直接观测到的源信号从被干扰和噪声污染的混合信号中分离出来，其凭借其强大的技术优势，在生理信号处理、图像处理等领域得到了广泛的应用。然而，在进行盲源分离时先验信息较少或无先验信息可用，存在观测信号通道不足、多数据集相互关联等难点亟待解决。项目针对欠定盲源分离这一新兴前沿研究方向开展探索，从信号的稀疏性和统计特性入手，研究混合矩阵的估计及源信号的恢复，并将盲源分离方法应用于真实信号中。具体研究工作包括：.1）针对观测信号易受噪声干扰，传统基于2阶统计量的欠定盲源分离结果对噪声较为敏感的问题，利用观测信号的3阶统计信息实现混合矩阵的估计。考虑到源信号的自相关特性，将多时延下观测信号的3阶统计信息堆叠成4阶张量，进而将混合矩阵估计问题转化为4阶张量的典范双峰分解问题。.2）针对生理信号中单信号源点较少，而传统基于单信号源点稀疏性的欠定盲源分离算法性能不佳的问题，提出了基于双数据源点的欠定盲源分离混合矩阵估计方法，放松了对信号稀疏性的依赖。.3）针对联合盲源分离时未考虑系统的欠定性，而欠定盲源分离时又忽视了数据集间的关联性的问题，提出基于信号统计特性的欠定联合盲源分离方法，并将其用于脑电信号去噪。.4）探索了盲源分离在心电信号、语音信号及脑电信号去噪中的应用，并与下游机器学习方法相结合实现了特定分类任务。.课题的研究综合了统计信号处理、机器学习和人工智能等多门学科，研究成果能够丰富盲源分离的相关理论，并可大幅提高欠定盲源分离时混合矩阵估计的精度，将相关方法应用于心电、语音等生理信号处理，具有重要的理论意义和实际应用价值。