基于四阶累积量张量联合对角化的多数据集联合盲源分离
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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。
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.
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.
引文
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[18]MOORD.Database for the identification of systems(DaISy)[OL]. http://www.esat.kuleuven.ac.be/sista/daisy,2010.
[19]DE LATHAUWER L, DE MOOR B, and VANDEWALLE J.Fetal electrocardiogram extraction by blindsource subspace separation[J]. IEEE Transactions on Biomedical Engineering, 2000, 47(5):567–572. doi:10.1109/78.950782.
[20]CARDOSO J F. Multidimensional independent component analysis[C]. IEEE International Conference on Acoustics,Speechand Signal Processing.Seattle,USA,1998:1941–1944. doi:10.1109/ICASSP.1998.681443.
[2]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.
[3]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/JEIT160209.CHEN 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.
[4]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.
[5]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/JEIT171156.FUWeihongandZHANGCong.Independentvector 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.
[6]GONG Xiaofeng,WANG Xiulin,and LIN Qiuhua.Generalized non-orthogonal joint diagonalization with LU decompositionandsuccessiverotations[J].IEEE Transactions on Signal Processing, 2015, 63(5):1322–1334.doi:10.1109/TSP.2015.2391074.
[7]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.
[8]COMON P and JUTTEN C. Handbook of Blind Source Separation:Independent Component Analysisand Applications[M]. Kidlington, UK Academic Press, Inc.,2010. doi:org/10.1016/C2009-0-19334-0.
[9]GONG Xiaofeng, LIN Qiuhua, CONG Fengyu, et al. Double coupled canonical polyadic decomposition for joint blind sourceseparation[J].IEEE Transactions on Signal Processing, 2018, 66(13):3475–3490. doi:10.1109/TSP.2018.2830317.
[10]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.
[11]MIAOJifei,CHENGGuanghui,CAIYufeng,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.
[12]HAROLD H. Relations between two sets of variates[J].Biometrika, 1936, 28(3/4):321–377. doi:10.2307/2333955.
[13]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.
[14]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. doi:10.1109/ICNC.2015.7377973.
[15]WANG Xiulin, GONG Xiaofeng, LIN Qiuhua. A study on parallelization of successive rotation based joint diagonalization[C]. International Conference on Digital SignalProcessing.HongKong,China,2014:1–5.doi:10.1109/ICDSP.2014.6900778.
[16]CARDOSO J F and SOULOUMIAC A. Blind beam forming 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.
[17]LI Yiou, ADALI T, and WANG Wei, et al. Joint blind sourceseparationbymultisetcanonicalcorrelation analysis[J]. IEEE Transactions on Signal Processing, 2009,57(10):3918–3929. doi:10.1109/TSP.2009.2021636.
[18]MOORD.Database for the identification of systems(DaISy)[OL]. http://www.esat.kuleuven.ac.be/sista/daisy,2010.
[19]DE LATHAUWER L, DE MOOR B, and VANDEWALLE J.Fetal electrocardiogram extraction by blindsource subspace separation[J]. IEEE Transactions on Biomedical Engineering, 2000, 47(5):567–572. doi:10.1109/78.950782.
[20]CARDOSO J F. Multidimensional independent component analysis[C]. IEEE International Conference on Acoustics,Speechand Signal Processing.Seattle,USA,1998:1941–1944. doi:10.1109/ICASSP.1998.681443.