Complexity Reduction of Eigenvalue Decomposition-Based Diffuse Power Spectral Density Estimators Using the Power Method

Abstract

In noisy and reverberant environments speech enhancement techniques such as the multi-channel Wiener filter (MWF) can be used to improve speech quality and intelligibility. Assuming that reverberation and ambient noise can be modeled as diffuse sound fields, such techniques require an estimate of the diffuse power spectral density (PSD). Recently a multi-channel diffuse PSD estimator based on the eigenvalue decomposition (EVD) of the prewhitened signal PSD matrix was proposed. The EVD-based PSD estimator is advantageous in comparison to other state-of-the-art PSD estimators, since it does not require knowledge of the relative early transfer functions of the target signal. However, computing the EVD can be computationally expensive, particularly when the number of microphones is large. In this paper we propose to reduce the complexity of the EVD-based PSD estimator by using the iterative power method to compute the eigenvalues. Since the EVD-based PSD estimator only requires the largest eigenvalues, the full EVD is not required and the power method is a well suited computationally efficient technique to estimate these eigenvalues. Experimental results show that using the PSD estimated via the power method in an MWF yields a very similar performance as using the PSD estimated via the full EVD.