Approximate Message Passing for Underdetermined Audio Source Separation

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.