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In this paper we address the problems of modeling the acoustic spacegenerated by a full-spectrum sound source and of using the learned model forthe localization and separation of multiple sources that simultaneously emitsparse-spectrum sounds. We lay theoretical and methodological grounds in orderto introduce the binaural manifold paradigm. We perform an in-depth study ofthe latent low-dimensional structure of the high-dimensional interauralspectral data, based on a corpus recorded with a human-like audiomotor robothead. A non-linear dimensionality reduction technique is used to show thatthese data lie on a two-dimensional (2D) smooth manifold parameterized by themotor states of the listener, or equivalently, the sound source directions. Wepropose a probabilistic piecewise affine mapping model (PPAM) specificallydesigned to deal with high-dimensional data exhibiting an intrinsic piecewiselinear structure. We derive a closed-form expectation-maximization (EM)procedure for estimating the model parameters, followed by Bayes inversion forobtaining the full posterior density function of a sound source direction. Weextend this solution to deal with missing data and redundancy in real worldspectrograms, and hence for 2D localization of natural sound sources such asspeech. We further generalize the model to the challenging case of multiplesound sources and we propose a variational EM framework. The associatedalgorithm, referred to as variational EM for source separation and localization(VESSL) yields a Bayesian estimation of the 2D locations and time-frequencymasks of all the sources. Comparisons of the proposed approach with severalexisting methods reveal that the combination of acoustic-space learning withBayesian inference enables our method to outperform state-of-the-art methods.

Acoustic Space Learning for Sound Source Separation and Localization on Binaural Manifolds