基于高阶累积量张量分解的联合盲源分离算法  

Joint Blind Source Separation Algorithm Based on Decomposition of Higher‐Order Cumulant Tensors

作　　者：季策 刘明欣 JI Ce;LIU Ming‐xin(School of Computer Science&Engineering,Northeastern University,Shenyang 110169,China)

机构地区：[1]东北大学计算机科学与工程学院,辽宁沈阳110169

出　　处：《东北大学学报（自然科学版）》2024年第1期26-32,共7页Journal of Northeastern University(Natural Science)

基　　金：中央高校基本科研业务费专项资金资助项目(N2116015,N2116020).

摘　　要：提出一种基于高阶累积量张量分解的联合盲源分离(JBSS)算法,该算法可以从多组数据集的观测信号中恢复出源信号.首先通过计算多组数据集观测信号的高阶互累积量张量,利用累积量张量潜在的对角结构,将JBSS问题转化为高阶张量CP分解(CPD)问题.接下来,通过张量列分解(TTD)将高阶张量分解为由不高于3阶的多个互连的核张量组成的简单张量网络,由此将高阶CPD问题转化为多个3阶CPD问题.最后,根据TTD与CPD之间的关系,在多次3阶CPD之后,通过依次对因子矩阵进行重新排序与缩放得到多数据集的混合矩阵,进而实现对源信号的分离.实验结果表明,该算法具有较快的运行速度.A joint blind source separation(JBSS)algorithm based on decomposition of high‐order cumulant tensors is proposed.The algorithm recovers the source signals from the observation signals of multiset data.Firstly,the higher‐order cross‐cumulant tensors of observation signals of multiset data are calculated.Due to the potential diagonal structures of cumulant tensors,the JBSS problem can be transformed into canonical polyadic decomposition(CPD)of a higher‐order tensor.Next,by tensor train decomposition(TTD),the higher‐order tensor is decomposed into a simple tensor network composed of a set of interconnected core tensors of orders not higher than 3.The CPD of a higher‐order tensor thereby is transformed into a set of CPDs of order‐3 tensors.Finally,according to the links between TTD and CPD,after several CPDs of order‐3 tensors,the mixed matrices of multi‐dataset can be obtained by reordering and rescaling the factor matrices sequentially,resulting in the separation of the source signals.Simulation results show that the proposed algorithm operated at a faster speed.

关 键 词：联合盲源分离 张量列分解 CP分解 高阶累积量 

分 类 号：TN911.7[电子电信—通信与信息系统]