Robust Dereverberation with Kronecker Product Based Multichannel Linear Prediction

Reverberation impairs not only the speech quality, but also intelligibility. The weighted-prediction-error (WPE) method, which estimates the late reverberation component based on a multichannel linear predictor, is by far one of the most effective algorithms for dereverberation. Generally, the WPE prediction filter in every short-Time-Fourier-Transform (STFT) subband has to be long enough to estimate accurately the late reverberation component. As a consequence, WPE is computationally expensive, which makes it difficult to implement into real-Time embedded or edge computing devices. Moreover, WPE is sensitive to additive noise and its performance may suffer from dramatic degradation even in environments where the signal-To-noise ratio (SNR) is high. To address these drawbacks, this letter proposes to decompose the multichannel linear prediction filter as a Kronecker product of a temporal (interframe) prediction filter and a spatial filter. An iterative algorithm is then developed to optimize the two filters. In comparison with the original WPE algorithm, the presented method not only exhibits better performance in terms of dereverberation and robustness to additive noise, as there are fewer parameters to estimate for a given number of observation signal samples, but is also computationally more efficient, since the dimensions of the covariance matrices after Kronecker product decomposition are smaller.