This paper focuses on single-channel semi-supervised speech enhancement. We learn a speaker-independent deep generative speech model using the framework of variational autoencoders. The noise model remains unsupervised because we do not assume prior knowledge of the noisy recording environment. In this context, our contribution is to propose a noise model based on alpha-stable distributions, instead of the more conventional Gaussian non-negative matrix factorization approach found in previous studies. We develop a Monte Carlo expectation-maximization algorithm for estimating the model parameters at test time. Experimental results show the superiority of the proposed approach both in terms of perceptual quality and intelligibility of the enhanced speech signal.
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