基于耦合张量分解的多数据集联合盲分离方法研究

Driven by the need of a number of applications, joint blind source separation (J-BSS) has recently become one of the hottest topics in signal processing. In the meantime, as an emerging tool for multi-set data fusion, coupled tensor decomposition has attracted much attention, thanks to its advantages over classical tensor decomposition techniques with regards to identifiability and accuracy. However, most of the existing works on coupled tensor decomposition requires the signal in each dataset satisfies by itself a particular tensor decomposition model, and is not applicable to J-BSS in the general sense, where the multi-set signal has matrix form. As such, the proposal aims at deep-going research on J-BSS based on coupled tensor decomposition, in the following three key aspects: mathematical modelization, identifiability analysis, and algorithms. We will also apply the to-be-developed J-BSS methods to two typical J-BSS problems: "multi-subject fMRI data analysis", and "wide band array signal direction of arrival estimation", to discover the advantages of coupled tensor decomposition based J-BSS over tensor based BSS. The research in the proposal will promote the development of J-BSS and tensor based signal processing. It will also provide theoretical and method backing for solving the multi-set data fusion problem in several key scientific areas such as brain recognition and wideband array processing, and therefore has rich theoretical significance and high application prospect.

在众多实际问题的驱动下，多数据集信号联合盲分离（J-BSS: Joint Blind Source Separation）已成为信号处理领域新的热点。同时，耦合张量分解作为一种极具潜力的多维数据融合工具，逐步获得人们关注，若能将其成功应用至J-BSS，将大大推动J-BSS 这项前沿技术的发展。然而现有分解方法通常要求各数据集自身即满足特定的张量模型，并不适合一般的、具有矩阵信号模型的J-BSS。为此，本项目拟针对基于耦合张量分解的J-BSS，在数学建模、辨识性分析、计算方法三方面开展深入研究，并探讨其在两种典型J-BSS问题：“多被试fMRI 数据分析”、“宽带阵列波达方向估计”中的应用，从理论和应用方面揭示其性能优势。本项目将推动张量信号处理、联合盲分离等前沿技术的发展，并为解决脑认知、宽带大规模阵列处理等关键技术领域中的多数据集融合问题提供理论与方法支撑，具有重要的理论价值与应用前景。

在众多实际问题的驱动下，多数据集信号联合盲分离（J-BSS: Joint Blind Source Separation）已成为信号处理领域新的热点。同时，耦合张量分解作为一种极具潜力的多维数据融合工具，近年来获得了人们广泛关注。本项目对基于耦合张量分解的J-BSS从理论、方法、应用三个层次开展了系统全面的研究，圆满完成研究任务。所取得的主要成果如下。(1) 提出一系列耦合张量化方法，通过利用多数据集信号在统计域和数据域的相似特征，建立了J-BSS问题的耦合张量分解模型；(2) 首次提出并证明了耦合张量分解的可唯一辨识条件，回答了J-BSS在可唯一辨识性方面的理论问题；(3) 提出一系列耦合张量分解代数类算法，若干广义联合对角化算法，基于交替最小二乘及非线性最小二乘的迭代优化类算法，上述算法统一构成了耦合张量分解的计算框架，有效解决了耦合张量分解的计算问题；(4) 将基于耦合张量分解的J-BSS算法成功应用于宽带阵列波达方向估计、多基地MIMO雷达目标定位、胎儿心电信号分离、多被试fMRI数据处理等应用方面，取得了一系列成果。.基于上述研究成果，项目组共发表SCI检索期刊论文7篇，JCR 1区论文5篇，最具代表性的研究成果发表在信号处理顶级期刊IEEE Transactions on Signal Processing，脑科学顶级期刊IEEE Transactions on Medical Imaging上面。授权发明专利4项，另有2项已获公开。培养博士1名，硕士10名。项目负责人受邀在IWEICT2019国际研讨会作大会主题报告，项目组成员多次参加国际会议作学术汇报。