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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LAHAT D, ADALI T, and JUTTEN C. Multimodal data fusion: An overview of methods, challenges, and prospects[J]. Proceedings of the IEEE, 2015, 103(9): 1449–1477. doi: 10.1109/JPROC.2015.2460697 STEYRL D, KRAUSZ G, KOSCHUTNIG K, et al. Reference Layer Adaptive Filtering (RLAF) for EEG artifact reduction in simultaneous EEG-fMRI[J]. Journal of Neural Engineering, 2017, 14(2): 026003. doi: 10.1088/1741-2552/14/2/026003 陈强, 陈勋, 余凤琼. 基于独立向量分析的脑电信号中肌电伪迹的去除方法[J]. 电子与信息学报, 2016, 38(11): 2840–2847. doi: 10.11999/JEIT160209CHEN Qiang, CHEN Xun, and YU Fengqiong. Removal of muscle artifact from EEG data based on independent vector analysis[J]. Journal of Electronics &Information Technology, 2016, 38(11): 2840–2847. doi: 10.11999/JEIT160209 KUANG Lidan, LIN Qiuhua, GONG Xiaofeng, et al. Adaptive independent vector analysis for multi-subject complex-valued fMRI data[J]. Journal of Neuroscience Methods, 2017, 281: 49–63. doi: 10.1016/j.jneumeth.2017.01.017 付卫红, 张琮. 基于步长自适应的独立向量分析卷积盲分离算法[J]. 电子与信息学报, 2018, 40(9): 2158–2164. doi: 10.11999/JEIT171156FU Weihong and ZHANG Cong. Independent vector analysis convolutive blind separation algorithm based on step-size adaptive[J]. Journal of Electronics &Information Technology, 2018, 40(9): 2158–2164. doi: 10.11999/JEIT171156 GONG Xiaofeng, WANG Xiulin, and LIN Qiuhua. Generalized non-orthogonal joint diagonalization with LU decomposition and successive rotations[J]. IEEE Transactions on Signal Processing, 2015, 63(5): 1322–1334. doi: 10.1109/TSP.2015.2391074 XING Ling, MA Qiang, and ZHU Min. Tensor semantic model for an audio classification system[J]. Science China (Information Sciences) , 2013, 56(6): 1–9. doi: 10.1007/s11432-013-4821-x COMON P and JUTTEN C. Handbook of Blind Source Separation: Independent Component Analysis and Applications[M]. Kidlington, UK Academic Press, Inc., 2010. GONG Xiaofeng, LIN Qiuhua, CONG Fengyu, et al. Double coupled canonical polyadic decomposition for joint blind source separation[J]. IEEE Transactions on Signal Processing, 2018, 66(13): 3475–3490. doi: 10.1109/TSP.2018.2830317 LI Xilin, ADALI T, and ANDERSON M. Joint blind source separation by generalized joint diagonalization of cumulant matrices[J]. Signal Processing, 2011, 91(10): 2314–2322. doi: 10.1016/j.sigpro.2011.04.016 MIAO Jifei, CHENG Guanghui, CAI Yufeng, et al. Approximate joint singular value decomposition algorithm based on Givens-like rotation[J]. IEEE Signal Processing Letters, 2018, 25(5): 620–624. doi: 10.1109/LSP.2018.2815584 HAROLD H. Relations between two sets of variates[J]. Biometrika, 1936, 28(3/4): 321–377. doi: 10.2307/2333955 DE LATHAUWER L, DE MOOR B, and VANDEWALLE J. Independent component analysis and (simultaneous) third-order tensor diagonalization[J]. IEEE Transactions on Signal Processing, 2001, 49(10): 2262–2271. doi: 10.1109/78.950782 LIU Yingliang, GONG Xiaofeng, and LIN Qiuhua. Non-orthogonal tensor diagonalization based on successive rotations and LU decomposition[C]. IEEE International Conference on Natural Computation. Zhangjiajie, China, 2015: 102–107. WANG Xiulin, GONG Xiaofeng, LIN Qiuhua. A study on parallelization of successive rotation based joint diagonalization[C]. International Conference on Digital Signal Processing. Hong Kong, China, 2014: 1–5. CARDOSO J F and SOULOUMIAC A. Blind beamforming for non-Gaussian signals[J]. IEE Proceedings F (Radar and Signal Processing) , 1993, 140(6): 362–370. doi: 10.1049/ip-f-2.1993.0054 LI Yiou, ADALI T, and WANG Wei, et al. Joint blind source separation by multiset canonical correlation analysis[J]. IEEE Transactions on Signal Processing, 2009, 57(10): 3918–3929. doi: 10.1109/TSP.2009.2021636 MOOR D. Database for the identification of systems (DaISy) [OL]. http://www.esat.kuleuven.ac.be/sista/daisy, 2010. DE LATHAUWER L, DE MOOR B, and VANDEWALLE J. Fetal electrocardiogram extraction by blind source subspace separation[J]. IEEE Transactions on Biomedical Engineering, 2000, 47(5): 567–572. doi: 10.1109/78.950782 CARDOSO J F. Multidimensional independent component analysis[C]. IEEE International Conference on Acoustics, Speech and Signal Processing. Seattle, USA, 1998: 1941–1944. -
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