Phase unmixing: Multichannel source separation with magnitude constraints

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.

Audio-motor integration for robot audition

“…Nevertheless, we noted that the computational bottleneck of this approach remains the non-convex estimation of the phase-corrections matrix Φ t . This difficult and general problem in audio, referred to as phase unmixing is the subject of current research [18].…”

Audio Source Separation with Magnitude Priors: The Beads Model

“…In that setting, the donut-shaped distribution shown in Figure 1b is much better than LGM because it gives its highest probability mass on the circle of radius b j (f, t). If σ = 0, we end up with the phase unmixing problem [15]. However, even with some uncertainty σ > 0, such a distribution suffers from non-tractability.…”