Joint Dereverberation and Separation with Iterative Source Steering

TL;DR

This paper introduces two new algorithms for joint dereverberation and blind source separation that reduce computational cost and improve stability by minimizing matrix inversions, while maintaining performance.

Contribution

It proposes two algorithms leveraging iterative source steering to mitigate matrix inversion issues in joint dereverberation and separation, with one being inversion-free.

Findings

Both methods achieve comparable performance to ILRMA-T.

Number of iterations needed is similar for two sources.

Algorithms are more computationally efficient and memory-friendly.

Abstract

We propose a new algorithm for joint dereverberation and blind source separation (DR-BSS). Our work builds upon the IRLMA-T framework that applies a unified filter combining dereverberation and separation. One drawback of this framework is that it requires several matrix inversions, an operation inherently costly and with potential stability issues. We leverage the recently introduced iterative source steering (ISS) updates to propose two algorithms mitigating this issue. Albeit derived from first principles, the first algorithm turns out to be a natural combination of weighted prediction error (WPE) dereverberation and ISS-based BSS, applied alternatingly. In this case, we manage to reduce the number of matrix inversion to only one per iteration and source. The second algorithm updates the ILRMA-T matrix using only sequential ISS updates requiring no matrix inversion at all. Its implementation is straightforward and memory efficient. Numerical experiments demonstrate that both methods achieve the same final performance as ILRMA-T in terms of several relevant objective metrics. In the important case of two sources, the number of iterations required is also similar.