Phase-Aware Non-negative Spectrogram Factorization

Non-negative spectrogram factorization has been proposed for single-channel source separation tasks. These methods operate on the magnitude or power spectrogram of the input mixture and estimate the magnitude or power spectrogram of source components. The usual assumption is that the mixture spectrogram is well approximated by the sum of source components. However, this relationship additionally depends on the unknown phase of the sources. Using a probabilistic representation of phase, we derive a cost function that incorporates this uncertainty. We compare this cost function against four standard approaches for a variety of spectrogram sizes, numbers of components, and component distributions. This phase-aware cost function reduces the estimation error but is more affected by detection errors.