  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 determini- stic and generic
uniqueness conditions for DC-CPD, which are shown to be more relaxed than their
CPD counterpart. 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.
