Decomposing audio into discrete sources, especially commercial tracks into stems. This is in large part a problem of data acquisition since artists do not usually release unmixed versions of their tracks.
The taxonomy here comes from Jordi Pons’ tutorial Waveform-based music processing with deep learning.
In the time domain, facebook’s demucs gets startlingly good performance on MusDB (startlingly good in that, if I have understood correctly, they train only on MusDB wccih is a very small data set compared to what the big players such as Spotify have access to, so they have very good priors.)
Spleeter is the Deezer source separation library with pretrained models written in Python and uses Tensorflow. It makes it easy to train source separation model (assuming you have a dataset of isolated sources), and provides already trained state of the art model for performing various flavour of separation :
- Vocals (singing voice) / accompaniment separation (2 stems)
- Vocals / drums / bass / other separation (4 stems)
- Vocals / drums / bass / piano / other separation (5 stems)
Wave-U-Net architectures seems popular if one wants to DIY.
GANs seem natural here, although most methods are supervised, or better, a probabilistic method.
Non-negative matrix factorisation approaches
Factorise the spectrogram! Authors such as (Virtanen 2007; Bertin, Badeau, and Vincent 2010; Vincent, Bertin, and Badeau 2008; Févotte, Bertin, and Durrieu 2008; Smaragdis 2004) popularised using non-negative matrix factorisations to identify the “activations” of power spectrograms for music analysis. It didn’t take long for this to be used in resynthesis tasks, by e.g. Aarabi and Peeters (2018), Buch, Quinton, and Sturm (2017) (source, site), Driedger and Pratzlich (2015) (site), Hoffman, Blei, and Cook (2010)). Of course, these methods leave you with a phase retrieval problem. These methods work really well in resyntheis, where you don not care so much about audio bleed.
Harmonic-percussive source separation
Harmonic Percussive separation. needs explanation. 🏗 (Tachibana, Ono, and Sagayama 2014; Driedger, Muller, and Ewert 2014; FitzGerald et al. 2013; Lakatos 2000; N. Ono et al. 2008; Fitzgerald 2010; Tachibana et al. 2012; Driedger, Müller, and Disch 2014; Ono et al. 2008; Schlüter and Böck 2014; Laroche et al. 2017; Elowsson and Friberg 2017; Driedger and Müller 2016)
That first step might be to find some model which can approximately capture the cyclic and disordered components of the signal. Indeed Metamorph and smstools, based on a “sinusoids+noise” model do this kind of decomposition, but they mostly use it for resynthesis in limited ways, not simulating realisations from the inferred model of an underlying stochastic process. There is an implementation in csound called ATS which looks interesting?
Some non-parametric conditional wavelet density sounds more fun to me, maybe as a Markov random field - although what exact generative model I would fit here is still opaque to me. The sequence probably possesses multiple at scales, and there is evidence that music might have a recursive grammatical structure which would be hard to learn even if we had a perfect decomposition.
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