Supplementations to the Higher Order Subspace Algorithm for Suppression of Spatially Colored Noise

Recently, researchers have proposed to represent the observed multichannel speech data as a 3-D tensor and then directly reduce the noise level in the time domain. For example, a higher order subspace algorithm (HOSA) was proposed for the reduction of spatially white noise (i.e., the noise added to different sensors is mutually uncorrelated) and yielded an excellent performance. Nevertheless, for spatially colored noise (i.e., the noise added to different sensors is correlated or even perfectly coherent), HOSA suffers from serious performance degradation because the T-weighted noise covariance matrix is not strictly diagonal any more. In this letter, we present three efficient supplementations to HOSA to improve its performance on spatially colored noise. First, we directly estimate the weighted signal covariance matrices by speech subtraction because noise statistics are unknown and have to be estimated in the case. Second, we clear all the off-diagonal elements of the whitened T-weighted noise covariance matrix as they generally have negligible absolute values. Third, we process speech frames in an overlap-free manner to better meet the white noise assumption. In both simulations and real experiments, these supplementations can greatly improve the performance of HOSA on spatially colored noise while not affecting its performance on spatially white noise.