Double Coupled Canonical Polyadic Decomposition for Joint Blind Source Separation

TL;DR

This paper introduces a novel algebraic method for joint blind source separation using double coupled canonical polyadic decomposition, providing deterministic solutions and improved uniqueness over existing methods.

Contribution

It proposes a new algebraic DC-CPD algorithm based on coupled rank-1 detection, with relaxed uniqueness conditions and superior performance in BSS tasks.

Findings

The algorithm provides exact solutions in noiseless scenarios.

DC-CPD shows improved uniqueness conditions compared to CPD.

Experimental results demonstrate superior accuracy over existing methods.

Abstract

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.