Gain-robust multi-pitch tracking using sparse nonnegative matrix factorization

While nonnegative matrix factorization (NMF) has successfully been applied for gain-robust multi-pitch detection, a method to track pitch values over time was not provided. We embed NMF-based pitch detection into a recently proposed pitch-tracking system, based on a factorial hidden Markov model (FHMM). The original system models speech spectra with Gaussian mixture models, which is sensitive to a gain mismatch between training and test data. We therefore combine the advantages of these two approaches and derive a gain-adaptive observation model for the FHMM. As training algorithm we use a modification of ℓ
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-sparse NMF, which represents the short-time spectrum with scalable basis vectors. In experiments we show that the new approach significantly increases the gain-robustness of the original tracking system.