  Audio inpainting, i.e., the task of restoring missing or occluded audio
signal samples, usually relies on sparse representations or autoregressive
modeling. In this paper, we propose to structure the spectrogram with
nonnegative matrix factorization (NMF) in a probabilistic framework. First, we
treat the missing samples as latent variables, and derive two
expectation-maximization algorithms for estimating the parameters of the model,
depending on whether we formulate the problem in the time- or time-frequency
domain. Then, we treat the missing samples as parameters, and we address this
novel problem by deriving an alternating minimization scheme. We assess the
potential of these algorithms for the task of restoring short- to middle-length
gaps in music signals. Experiments reveal great convergence properties of the
proposed methods, as well as competitive performance when compared to
state-of-the-art audio inpainting techniques.
