Phase Unmixing : Multichannel Source Separation with Magnitude Constraints

TL;DR

This paper addresses the challenging problem of phase estimation in multichannel source separation, proposing three methods including a convex relaxation that outperforms traditional filters, especially in under-determined scenarios.

Contribution

It introduces three novel approaches for phase unmixing, notably a convex relaxation method that can achieve exact separation in complex under-determined cases.

Findings

Convex relaxation outperforms oracle Wiener filter in simulations.

Alternate minimization surpasses traditional methods in under-determined tasks.

Potential for exact source separation with the proposed convex approach.

Abstract

We consider the problem of estimating the phases of K mixed complex signals from a multichannel observation, when the mixing matrix and signal magnitudes are known. This problem can be cast as a non-convex quadratically constrained quadratic program which is known to be NP-hard in general. We propose three approaches to tackle it: a heuristic method, an alternate minimization method, and a convex relaxation into a semi-definite program. The last two approaches are showed to outperform the oracle multichannel Wiener filter in under-determined informed source separation tasks, using simulated and speech signals. The convex relaxation approach yields best results, including the potential for exact source separation in under-determined settings.