Analysis of signal mixtures is an elementary problem found in application domains specific to various signal modalities. For musical audio signals specifically, it presents a step fundamental to many subsequent tasks in the Music Information Retrieval, such as music transcription or instrument identification and extraction. The underlying goal is often to identify the sources present in the mixture, potentially along with their various properties. In the context of musical signals, atomicity of signal sources can also be defined at various levels. A central difficulty stems from the combinatorial nature of the problem, as music allows for a large number of atomic sources with varying degrees of polyphony (concurrency of source activity across time). We aim to address the combinatorial nature of the problem by analysing mixtures through linear decomposition, while leveraging advances on the front of deep bijective models of data density (e.g., "normalizing flows") in order to better express individual sources by modelling them independently.

* Supervisor: Gerhard Widmer, JKU Linz, Austria
* Dates: 01 October 2019 – Ongoing