Double Coupled Canonical Polyadic Decomposition for Joint Blind Source Separation

摘要

Joint blind source separation (J-BSS) is an emerging data-driven techniquefor multi-set data-fusion. In this paper, J-BSS is addressed from a tensorialperspective. We show how, by using second-order multi-set statistics in J-BSS,a specific double coupled canonical polyadic decomposition (DC-CPD) problem canbe formulated. We propose an algebraic DC-CPD algorithm based on a coupledrank-1 detection mapping. This algorithm converts a possibly underdeterminedDC-CPD to a set of overdetermined CPDs. The latter can be solved algebraicallyvia a generalized eigenvalue decomposition based scheme. Therefore, thisalgorithm is deterministic and returns the exact solution in the noiselesscase. In the noisy case, it can be used to effectively initialize optimizationbased DC-CPD algorithms. In addition, we obtain the determini- stic and genericuniqueness conditions for DC-CPD, which are shown to be more relaxed than theirCPD counterparts. Experiment results are given to illustrate the superiority ofDC- CPD over standard CPD with regards to uniqueness and accuracy.