欠定盲信号分离的高阶张量分析方法研究

Blind Source Separation (BSS), which is very important both in theory and practice, has found many potential applications in signal processing filed. Due to this, it has received a lot of attention around the world recently. However, the underdetermined BSS problem is very challenging and remains unsolved largely nowadays, where the higher-order tensor analysis is potentially a powerful tool to solve this problem. Exploiting the multi-linearity between higher-order cumulants of the mixtures and mixing matrix, this project focuses on the higher-order tensor decomposition methods for underdetermined BSS and solving several challenging problems as follows:.1).Identifying the number of sources in underdetermined BSS, which is equivalent to estimate the number of columns of mixing matrix in blind separation of sparse sources;.2).Blind identifying the mixing channels in underdetermined BSS, or estimating the cluster centroids if we solve the blind separation of sparse sources by clustering methods;.3).Developing more efficient higher-order tensor decomposition algorithms for underdetermined BSS problem and building rigorous convergence theory for them..In addition, currently we expect to find more applications and more successful applications for BSS in spite of its advances. In this project, we would like to investigate this problem and develop much more successful real-applications for BSS.

盲信号处理是现代信号处理中具有重要理论价值和巨大潜在应用的新学科分支，近年来一直是国内外关注的热点，而欠定混叠的盲信号分离是其中的难点问题。本课题针对信号向量的高阶统计量恰好为具有超对称结构的高阶张量的特性，探讨利用高阶张量分析方法挖掘隐藏在信号中的高阶频谱，致力于解决欠定盲信号分离研究中的几个关键问题： 1..欠定盲信号分离中源信号数目的盲估计问题（或稀疏信号盲分离中信道聚类分析的类数目估计问题）；.2..欠定盲信号分离中传输信道的盲辨识问题（或稀疏信号盲分离中信道聚类分析的类中心估计问题）；.3..相应于高阶张量分析方法的欠定盲信号分离算法及收敛性分析问题。.并尝试性的探讨盲信号分离的具体实际应用问题（因为目前这方面还没有真正的实际应用案例）。

盲信号处理是现代信号处理中具有重要理论价值和巨大潜在应用的新学科分支，近年来一直是国内外关注的热点，而欠定混叠的盲信号分离是其中的难点问题。本课题针对信号向量的高阶统计量恰好为具有超对称结构的高阶张量的特性，探讨利用高阶张量分析方法挖掘隐藏在信号中的高阶频谱，致力于解决欠定盲信号分离研究中的几个关键问题。课题组利用超对称张量平行因子分析这一数学工具的新发展，提出了一种新的CPD方法，这种方式不仅有较高的效率，避免经常展开到N模式，并且有希望籍此攻克高共线性瓶颈问题；开展了非负Tucker分解理论研究，建立了一种高效的非负Tucker分解算法，并成功应用于盲信号分离，大幅度降低了计算复杂度，同时抗噪能力强，是解决非负盲信号分离的有效工负盲信号分离的有效工具；课题组将盲信号处理的理论以及方法应用于胎儿心电图分析仪中，该方法的应用不仅为新的胎儿心电图分析仪提供了坚实的理论基础，而且获得了较以前更纯的胎儿心电信号。利用该项技术与相关企业合作研制的“新型胎心电检测仪”，目前已在广东省多所医院进行临床试验，取得了比较好的效果。

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