Robust Multichannel Dereverberation using Relaxed Multichannel Least Squares

A novel approach is proposed for robust multichannel dereverberation in the presence of system identification error (SIEs), based on channel shortening. A mathematical link is derived between the well known multiple-input/output inverse theorem (MINT) algorithm and channel shortening. The relaxed multichannel least squares (RMCLS) algorithm is then proposed as an efficient realization within the channel shortening paradigm and is shown through experimental results to outperform MINT in the presence of SIEs. While the RMCLS is robust to SIEs, the coloration of the output cannot be controlled. Two extensions to RMCLS are proposed to control the level of coloration and the performances of both extensions are evaluated comparatively. It is shown that both substantially maintain the dereverberation performance and robustness to SIEs obtained from RMCLS while effectively controlling the level of coloration introduced.