Relative Transfer Matrix Estimator using Covariance Subtraction

TL;DR

This work addresses blind estimation of the Relative Transfer Matrix (ReTM) for multiple simultaneous sources in reverberant, noisy environments. It introduces a covariance-subtraction approach to estimate the ReTM for a selected set of independent sources, avoiding the need to count sources or rely on inactivity. The proposed estimator is applied to a speaker-separation task and benchmarked against ReTF-based and oracle ReTM methods in both simulated and real rooms, demonstrating strong separation performance at very low SNRs, particularly in terms of SIR and STOI. The findings show that covariance-based ReTM estimation can be practical and effective for robust multi-source audio processing, with future potential for applications such as sound-zone control; mathematical formalism is provided for decomposing covariances into source-specific contributions and generalizing ReTM estimation to select source subsets.

Abstract

The Relative Transfer Matrix (ReTM), recently introduced as a generalization of the relative transfer function for multiple receivers and sources, shows promising performance when applied to speech enhancement and speaker separation in noisy environments. Blindly estimating the ReTM of sound sources by exploiting the covariance matrices of multichannel recordings is highly beneficial for practical applications. In this paper, we use covariance subtraction to present a flexible and practically viable method for estimating the ReTM for a select set of independent sound sources. To show the versatility of the method, we validated it through a speaker separation application under reverberant conditions. Separation performance is evaluated at low signal-to-noise ratio levels in comparison with existing ReTM-based and relative transfer function-based estimators, in both simulated and real-life environments.