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I have been doing some multimodal signal analysis, and sometimes ICA is used for detecting statistically independent components.

From my understanding, say if you have 2 sources and 2 receivers/sensors, you can have a unique solution, however if you have, say thousands of source, like in EEG, and 32 sensors, you need mathematically limiting tools to get to that approximate solution based on the context.

However, I kept wondering for example, if you are able to distinguish between 3 instruments in a song, from one track? so one sensor? Is there any research area to do with this? If yes, could you please direct me towards the right direction?

I am interested in statistical methods. I have already read a paper that used deep learning on music tracks that have the combined version and each instruments independent sounds, and ofc, uses them as input data, I am not interested in this.

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Some use the Frequency-Time representation as an additional source and try to do what you ask.

Some papers on that:

  1. Single Channel Source Separation with ICA Based Time-Frequency Decomposition (PDF Source).
  2. Musical Source Separation: An Introduction.

By the way, at the end, probably Deep Learning will yield the best results for this kind of task.

Pay attention that while the ICA model assumes very little on the mixed signals while in return it demands the number of signals to match or be higher than the number of sources. When there is a single signal (A single mix of the sources) you'd need to add some prior on the data (Side information). In Music it might be achievable (Like having different frequencies to different instruments).

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If you are interested about the state of the art I would suggest you to read about chimes. This was submitted to the Deep Noise Suppression challenge at interspeech 2020. You can also search for the other submissions if you want, you can see the results of the challenged are here.

Links accessed at Aug 11th 2021

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