Low-Complexity Kalman filter for multi-channel linear-prediction-based blind speech dereverberation

Abstract

Multi-channel linear prediction (MCLP) has been shown to be a suitable framework for tackling the problem of blind speech dereverberation. In recent years, a number of adaptive MCLP algorithms have been proposed, whereby the majority operates in the short-time Fourier transform (STFT) domain. In this paper, we focus on the STFT-based Kalman filter solution to the adaptive MCLP task. Similarly to all other available adaptive STFT-based MCLP algorithms, the Kalman filter exhibits a quadratic computational cost in the number of filter coefficients per frequency bin. Aiming at a reduced complexity, we propose to simplify to the Kalman filter solution by enforcing the state error correlation matrix to be block-diagonal, leading to a linear cost instead. Further, we apply a Wiener-gain spectral post-processor subsequent to MCLP, which is designed from readily available power spectral density (PSD) estimates. The convergence behavior of the standard and the simplified algorithm is evaluated by means of two objective measures, i.e. perceptual evaluation of speech quality (PESQ) and short-time objective intelligibility (STOI), showing only a minor performance degradation for the simplified algorithm.