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.

翻译：音频涂色, 即恢复缺失或隐蔽的音频信号样本的任务, 通常依赖于稀有的表示或自动递减模型。 在本文中, 我们提议在概率框架内以非负矩阵因子化( NMF) 构建光谱图。 首先, 我们将缺失的样本作为潜在变量, 并得出两种预期- 最大化算法来估计模型参数, 取决于我们是在时间- 频率域还是时间- 频率域内提出问题 。 然后, 我们将缺失的样本作为参数处理, 我们通过生成一个交替最小化计划来解决这个新问题。 我们评估这些算法对于恢复音乐信号中短至中长度差距的任务的潜力。 实验揭示了拟议方法的巨大趋同性, 以及与最新音频绘制技术相比, 以及竞争性的性表现。