Precise Dereverberation Using Multichannel Linear Prediction

In this paper, we discuss the numerical problems posed by the previously reported LInear-predictive Multi-input Equalization (LIME) algorithm when dealing with dereverberation of long room transfer functions (RTF). The LIME algorithm consists of two steps. First, a speech residual is calculated using multichannel linear prediction. The residual is free from the room reverberation effect but it is also excessively whitened because the average speech characteristics have been removed. In the second step, LIME estimates such average speech characteristics to compensate for the excessive whitening. When multiple microphones are used, the speech characteristics are common to all microphones whereas the room reverberation differs for each microphone. LIME estimates the average speech characteristics as the characteristics that are common to all the microphones. Therefore, LIME relies on the hypothesis that there are no zeros common to all channels. However, it is known that RTFs have a large number of zeros close to the unit circle on the z-plane. Consequently, the zeros of the RTFs are distributed in the same regions of the z-plane and, if an insufficient number of microphones are used, the channels would present numerically overlapping zeros. In such a case, the dereverberation algorithm would perform poorly. We discuss the influence of overlapping zeros on the dereverberation performance of LIME. Spatial information can be used to deal with the problem of overlapping zeros. By increasing the number of microphones, the number of overlapping zeros decreases and the dereverberation performance is improved. We also examine the use of cepstral mean normalization for post-processing to reduce the remaining distortions caused by the overlapping zeros