Blind Source Separation with Optimal Transport Non-negative Matrix Factorization

TL;DR

This paper introduces an optimal transport-based non-negative matrix factorization method for supervised speech blind source separation, improving perceptual quality by incorporating human sound perception into the separation process.

Contribution

It develops a novel optimal transport NMF algorithm that leverages perceptually meaningful frequency costs, advancing speech BSS and cross-domain sound processing.

Findings

Perceptually better voice reconstruction compared to Euclidean NMF

Effective in blind source separation tasks

Applicable to cross-domain sound processing

Abstract

Optimal transport as a loss for machine learning optimization problems has recently gained a lot of attention. Building upon recent advances in computational optimal transport, we develop an optimal transport non-negative matrix factorization (NMF) algorithm for supervised speech blind source separation (BSS). Optimal transport allows us to design and leverage a cost between short-time Fourier transform (STFT) spectrogram frequencies, which takes into account how humans perceive sound. We give empirical evidence that using our proposed optimal transport NMF leads to perceptually better results than Euclidean NMF, for both isolated voice reconstruction and BSS tasks. Finally, we demonstrate how to use optimal transport for cross domain sound processing tasks, where frequencies represented in the input spectrograms may be different from one spectrogram to another.