This paper presents theoretical and experimental results about constrained non-negative matrix factorization (NMF) to model the excitation of the musical instruments. These excitations represent vibrating objects, while the filter represents the resonance structure of the instrument, which colors the produced sound. We propose to model the excitations as the weighted sum of harmonically constrained basis functions, whose parameters are tied across different pitches of an instrument. An NMF-based framework is used to learn the model parameters. We assume that the excitations of a well-tempered instrument should possess an identifiable characteristic structure whereas the conditions of the music scene might produce variations in the filter. In order to test the reliability of our proposal, we evaluate our method for a music transcription task in two scenarios. On the first one, comparison with state-of-the-art methods has been performed over a dataset of piano recordings obtaining more accurate results than other NMF-based algorithms. On the second one, two woodwind instrument databases have been used to demonstrate the benefits of our model in comparison with previous excitation-filter model approaches.

Nonnegative matrix factorization (NMF) has been traditionally considered a promising approach for audio source separation. While standard NMF is only suited for single-channel mixtures, extensions to consider multi-channel data have been also proposed. Among the most popular alternatives, multichannel NMF (MNMF) and further derivations based on constrained spatial covariance models have been successfully employed to separate multi-microphone convolutive mixtures. This letter proposes a MNMF extension by considering a mixture model with Ray-Space-transformed signals, where magnitude data successfully encodes source locations as frequency-independent linear patterns. We show that the MNMF algorithm can be seamlessly adapted to consider Ray-Space-transformed data, providing competitive results with recent state-of-the-art MNMF algorithms in a number of configurations using real recordings.

In this paper, unsupervised learning is used to separate percussive and harmonic sounds from monaural non-vocal polyphonic signals. Our algorithm is based on a modified non-negative matrix factorization (NMF) procedure that no labeled data is required to distinguish between percussive and harmonic bases because information from percussive and harmonic sounds is integrated into the decomposition process. NMF is performed in this process by assuming that harmonic sounds exhibit spectral sparseness (narrowband sounds) and temporal smoothness (steady sounds), whereas percussive sounds exhibit spectral smoothness (broadband sounds) and temporal sparseness (transient sounds). The evaluation is performed using several real-world excerpts from different musical genres. Comparing the developed approach to three current state-of-the art separation systems produces promising results.

Close-microphone techniques are extensively employed in many live music recordings, allowing for interference rejection and reducing the amount of reverberation in the resulting instrument tracks. However, despite the use of directional microphones, the recorded tracks are not completely free from source interference, a problem which is commonly known as microphone leakage. While source separation methods are potentially a solution to this problem, few approaches take into account the huge amount of prior information available in this scenario. In fact, besides the special properties of close-microphone tracks, the knowledge on the number and type of instruments making up the mixture can also be successfully exploited for improved separation performance. In this paper, a nonnegative matrix factorization (NMF) method making use of all the above information is proposed. To this end, a set of instrument models are learnt from a training database and incorporated into a multichannel extension of the NMF algorithm. Several options to initialize the algorithm are suggested, exploring their performance in multiple music tracks and comparing the results to other state-of-the-art approaches.