# Multichannel Online Dereverberation based on Spectral Magnitude Inverse Filtering

## TL;DR

This paper introduces a robust online multichannel dereverberation method in the STFT domain that effectively suppresses reverberation, even with moving speakers, by using spectral magnitude inverse filtering based on a nonnegative convolution model.

## Contribution

It proposes a novel online dereverberation approach using spectral magnitude inverse filtering and a nonnegative CTF model, improving robustness against CTF perturbations and speaker movement.

## Key findings

- Effective reverberation suppression demonstrated in speech enhancement.
- Improved automatic speech recognition performance.
- Robustness against moving speakers.

## Abstract

This paper addresses the problem of multichannel online dereverberation. The proposed method is carried out in the short-time Fourier transform (STFT) domain, and for each frequency band independently. In the STFT domain, the time-domain room impulse response is approximately represented by the convolutive transfer function (CTF). The multichannel CTFs are adaptively identified based on the cross-relation method, and using the recursive least square criterion. Instead of the complex-valued CTF convolution model, we use a nonnegative convolution model between the STFT magnitude of the source signal and the CTF magnitude, which is just a coarse approximation of the former model, but is shown to be more robust against the CTF perturbations. Based on this nonnegative model, we propose an online STFT magnitude inverse filtering method. The inverse filters of the CTF magnitude are formulated based on the multiple-input/output inverse theorem (MINT), and adaptively estimated based on the gradient descent criterion. Finally, the inverse filtering is applied to the STFT magnitude of the microphone signals, obtaining an estimate of the STFT magnitude of the source signal. Experiments regarding both speech enhancement and automatic speech recognition are conducted, which demonstrate that the proposed method can effectively suppress reverberation, even for the difficult case of a moving speaker.