Joint Blind Source Separation Based on Joint Diagonalization of Fourth-order Cumulant Tensors
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摘要:
该文提出一种基于四阶累积量张量联合对角化的联合盲源分离(J-BSS)算法。首先通过计算4阶互累积量将多数据集信号的J-BSS问题转化为4阶张量联合对角化问题。接下来，基于雅可比连续旋转将张量联合对角化这类非线性优化问题，转化为一系列可获取闭式解的简单子优化问题，并通过交替迭代对多数据集混合矩阵进行更新，进而实现J-BSS。实验结果表明，所提算法具有良好的收敛性能，较之现有的同类型BSS及J-BSS算法具有更高的精度。此外，该算法在分离实际胎儿心电信号方面也表现出良好的性能。
Abstract:A new Joint Blind Source Separation (J-BSS) algorithm is proposed based on joint diagonalization of fourth-order cumulant tensors. This algorithm constructs first a set of fourth-order tensors by computing the fourth-order cross cumulant of the multiset signals. Then, based on the Jacobian successive rotation strategy, the highly nonlinear optimization problem of joint tensor diagonalization is transformed into a series of simple sub-optimization problems, each admitting a closed form solution. The multiset mixing matrices are hence updated via alternating iterations, which diagonalize jointly the data tensors. Simulation results show that the proposed algorithm has nice convergence pattern and higher accuracy than existing BSS and J-BSS algorithms of a similar type. In addition, the algorithm works well in a real-world application to fetal ECG separation.
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表 1 基于雅克比旋转的四阶张量联合对角化算法
输入： K个满足式(5)的张量${\mathcal{T}_1},{\mathcal{T}_{\rm{2}}},·\!·\!·,{\mathcal{T}_K} \in {\mathbb{C}^{R \times R \times R \times R}}$。 对因子矩阵进行初始化，进行如下步骤，直至收敛。 令i从1至$R - 1$变化， j从i +1至R变化，对固定索引(i, j)：
(1)根据式(16)，计算矩阵${\tilde{ G}}_{i,j}^{(m)},m = 1,2,3,4$；(2)根据式(10)，更新矩阵${{\tilde{ U}}^{(m)}}$及${T_1},{T_2},·\!·\!·,{T_K}$。 输出： 4个因子矩阵估计值${{\tilde{ U}}^{(1)}},{{\tilde{ U}}^{(2)}},{{\tilde{ U}}^{(3)}},{{\tilde{ U}}^{(4)}}$。 
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