期刊
IEEE TRANSACTIONS ON SIGNAL PROCESSING
卷 66, 期 13, 页码 3475-3490出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2018.2830317
关键词
Joint blind source separation; tensor; coupled canonical polyadic decomposition
资金
- National Natural Science Foundation of China [61671106, 61331019, 61379012, 81471742]
- Scientific Research Fund of Liaoning Education Department [L2014016]
- Fundamental Research Funds for the Central Universities [DUT16QY07]
- Research Council KU Leuven: C1 project [C16/15/059-nD]
- FWO: project [G.0830.14N, G.0881.14N]
- EOS project [G0F6718N]
- European Research Council under the European Union/ERC Advanced Grant BIOTENSORS [339804]
Joint blind source separation (J-BSS) is an emerging data-driven technique for multi-set data-fusion. In this paper, J-BSS is addressed from a tensorial perspective. We show how, by using second-order multi-set statistics in J-BSS, a specific double coupled canonical polyadic decomposition (DC-CPD) problem can be formulated. We propose an algebraic DC-CPD algorithm based on a coupled rank-1 detection mapping. This algorithm converts a possibly underdetermined DC-CPD to a set of overdetermined CPDs. The latter can be solved algebraically via a generalized eigenvalue decomposition based scheme. Therefore, this algorithm is deterministic and returns the exact solution in the noiseless case. In the noisy case, it can be used to effectively initialize optimization based DC-CPD algorithms. In addition, we obtain the deterministic and generic uniqueness conditions for DC-CPD, which are shown to be more relaxed than their CPD counterpart. We also introduce optimization based DC-CPD methods, including alternating least squares, and structured data fusion based methods. Experiment results are given to illustrate the superiority of DC-CPD over standard CPD based BSS methods and several existing J-BSS methods, with regards to uniqueness and accuracy.
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