基于四階累積量張量聯(lián)合對角化的多數(shù)據(jù)集聯(lián)合盲源分離
doi: 10.11999/JEIT180414
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大連理工大學信息與通信工程學院 ??大連 ??116024
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北京理工大學信息與電子學院 ??北京 ??100081
Joint Blind Source Separation Based on Joint Diagonalization of Fourth-order Cumulant Tensors
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School of Information and Communication Engineering, Dalian University of Technology, Dalian 116024, China
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School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China
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摘要:
該文提出一種基于四階累積量張量聯(lián)合對角化的聯(lián)合盲源分離(J-BSS)算法。首先通過計算4階互累積量將多數(shù)據(jù)集信號的J-BSS問題轉(zhuǎn)化為4階張量聯(lián)合對角化問題。接下來,基于雅可比連續(xù)旋轉(zhuǎn)將張量聯(lián)合對角化這類非線性優(yōu)化問題,轉(zhuǎn)化為一系列可獲取閉式解的簡單子優(yōu)化問題,并通過交替迭代對多數(shù)據(jù)集混合矩陣進行更新,進而實現(xiàn)J-BSS。實驗結(jié)果表明,所提算法具有良好的收斂性能,較之現(xiàn)有的同類型BSS及J-BSS算法具有更高的精度。此外,該算法在分離實際胎兒心電信號方面也表現(xiàn)出良好的性能。
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關(guān)鍵詞:
- 聯(lián)合盲源分離 /
- 聯(lián)合張量對角化 /
- 4階累積量
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 基于雅克比旋轉(zhuǎn)的四階張量聯(lián)合對角化算法
輸入: K個滿足式(5)的張量T1,T2,···,TK∈CR×R×R×R。 對因子矩陣進行初始化,進行如下步驟,直至收斂。 令i從1至R−1變化, j從i +1至R變化,對固定索引(i, j):
(1)根據(jù)式(16),計算矩陣˜G(m)i,j,m=1,2,3,4;(2)根據(jù)式(10),更新矩陣˜U(m)及T1,T2,···,TK。 輸出: 4個因子矩陣估計值˜U(1),˜U(2),˜U(3),˜U(4)。 下載: 導出CSV
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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 陳強, 陳勛, 余鳳瓊. 基于獨立向量分析的腦電信號中肌電偽跡的去除方法[J]. 電子與信息學報, 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 付衛(wèi)紅, 張琮. 基于步長自適應的獨立向量分析卷積盲分離算法[J]. 電子與信息學報, 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. -