Phase Unmixing : Multichannel Source Separation with Magnitude Constraints
This addresses a specific challenge in multichannel source separation for signal processing applications, but is incremental as it builds on known methods with constraints.
The paper tackled the problem of estimating phases of mixed complex signals when magnitudes and mixing matrix are known, proposing three methods including a convex relaxation that outperforms an oracle Wiener filter in under-determined source separation tasks, achieving exact separation in some cases.
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.