Approximate Message Passing for Underdetermined Audio Source Separation

TL;DR

This paper explores the use of approximate message passing algorithms, specifically AMP and VAMP, for separating multiple audio sources from underdetermined mixtures in the time-frequency domain, demonstrating promising artefact suppression.

Contribution

It introduces a block-based AMP approach for audio source separation and evaluates AMP and VAMP algorithms in this context, highlighting their effectiveness.

Findings

AMP and VAMP effectively suppress artefacts

The block-based approach improves separation quality

Algorithms are computationally efficient and converge quickly

Abstract

Approximate message passing (AMP) algorithms have shown great promise in sparse signal reconstruction due to their low computational requirements and fast convergence to an exact solution. Moreover, they provide a probabilistic framework that is often more intuitive than alternatives such as convex optimisation. In this paper, AMP is used for audio source separation from underdetermined instantaneous mixtures. In the time-frequency domain, it is typical to assume a priori that the sources are sparse, so we solve the corresponding sparse linear inverse problem using AMP. We present a block-based approach that uses AMP to process multiple time-frequency points simultaneously. Two algorithms known as AMP and vector AMP (VAMP) are evaluated in particular. Results show that they are promising in terms of artefact suppression.