  This paper presents a statistical method of single-channel speech enhancement
that uses a variational autoencoder (VAE) as a prior distribution on clean
speech. A standard approach to speech enhancement is to train a deep neural
network (DNN) to take noisy speech as input and output clean speech. Although
this supervised approach requires a very large amount of pair data for
training, it is not robust against unknown environments. Another approach is to
use non-negative matrix factorization (NMF) based on basis spectra trained on
clean speech in advance and those adapted to noise on the fly. This
semi-supervised approach, however, causes considerable signal distortion in
enhanced speech due to the unrealistic assumption that speech spectrograms are
linear combinations of the basis spectra. Replacing the poor linear generative
model of clean speech in NMF with a VAE---a powerful nonlinear deep generative
model---trained on clean speech, we formulate a unified probabilistic
generative model of noisy speech. Given noisy speech as observed data, we can
sample clean speech from its posterior distribution. The proposed method
outperformed the conventional DNN-based method in unseen noisy environments.
