The tabla is a pitched percussion instrument, which means that both the drums can be struck in ways that produce sustained, harmonic sounds. While the harmonics may be too few on the bass drum (thereby giving rise to only a low-pitched hum and not a strongly pitched sound), the treble drum generally produces at least 4-5 harmonics.
These drums can and are also often struck in ways that produce non-sustained, damped sounds. Playing compositions or accompaniment to a lead artist involves playing these sustained (or resonant) and damped strokes in various sequential combinations.
Matrix factorization techniques are a popular class of algorithms used in machine learning problems to decompose and transform data into components that may have certain desirable properties. This process of decomposition is usually carried out by applying some constraints on the resulting components to make them more interpretable. Non-negative matrix factorization(NMF), for instance, requires that the components/factors have non-negative elements only. This offers certain useful representations in the case where the data is say, a magnitude spectrogram.
Tabla music makes a good case for NMF-based source separation because of the overlap that arises between consecutive sounds when one drum is struck before a sustained sound on the other drum has completely faded. And since the vocabulary and the set of timbres produced by the tabla is fairly fixed, spectro-temporal templates for each stroke on the instrument can be learned and then used to decompose a recording of a composition played on the same instrument. Furthermore, if the exact sequence of strokes being played is known, then that can also be used to inform and improve the decomposition.
Another cool application here could be to use the separated components and modify them in some musically meaningful, expressive ways and then resynthesize the audio!
Rohit M. A., Preeti Rao, "Separation of Tabla Strokes from Tabla Solo Audios Using Non-negative Matrix Factorization", May 2019, Technical report - PDF