Solving Time-Domain Audio Inverse Problems Using Nonnegative Tensor Factorization

Nonnegative matrix factorization (NMF) and nonnegative tensor factorization (NTF) are important tools for modeling nonnegative data, which gained increasing popularity in various fields, a significant one of which is audio processing. However, there are still many problems in audio processing, for which the NMF (or NTF) model has not been successfully utilized. In this paper, we propose a new algorithm based on the NMF (and NTF) in the short-time Fourier domain for solving a large class of audio inverse problems with missing or corrupted time-domain samples. The proposed approach overcomes the difficulty of employing a model in the frequency domain to recover time-domain samples with the help of probabilistic modeling. Its performance is demonstrated for the following applications: audio declipping and declicking (never solved with NMF/NTF modeling prior to this paper); joint audio declipping/declicking and source separation (never solved with NMF/NTF modeling or any other method prior to this paper); and compressive sampling recovery and compressive sampling-based informed source separation (an extremely low complexity encoding scheme that is possible with the proposed approach and has never been proposed prior to this paper).