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Phase Unmixing : Multichannel Source Separation with Magnitude Constraints

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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.
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Dates and versions

hal-01372418 , version 1 (27-09-2016)
hal-01372418 , version 2 (13-03-2017)

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Antoine Deleforge, Yann Traonmilin. Phase Unmixing : Multichannel Source Separation with Magnitude Constraints. 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Mar 2017, New Orleans, United States. ⟨hal-01372418v2⟩
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