Maximum Likelihood PSD Estimation for Speech Enhancement in Reverberation and Noise

Abstract

In this contribution we focus on the problem of power spectral density (PSD) estimation from multiple microphone signals in reverberant and noisy environments. The PSD estimation method proposed in this paper is based on the maximum likelihood (ML) methodology. In particular, we derive a novel ML PSD estimation scheme that is suitable for sound scenes which besides speech and reverberation consist of an additional noise component whose second-order statistics are known. The proposed algorithm is shown to outperform an existing similar algorithm in terms of PSD estimation accuracy. Moreover, it is shown numerically that the mean squared estimation error achieved by the proposed method is near the limit set by the corresponding Cramér-Rao lower bound. The speech dereverberation performance of a multi-channel Wiener filter (MWF) based on the proposed PSD estimators is measured using several instrumental measures and is shown to be higher than when the competing estimator is used. Moreover, we perform a speech intelligibility test where we demonstrate that both the proposed and the competing PSD estimators lead to similar intelligibility improvements.

ML Estimation and CRBs for Reverberation, Speech, and Noise PSDs in Rank-Deficient Noise Field

“…In the blocking-based method, the desired speech signal is first blocked using a blocking matrix (BM), and then the reverberation PSD is estimated. Estimators in this class are also based on the ML approach [1], [5], [7], [9] or the LS criteria [2], [4].…”

“…In the noisy case, quality assessment was discussed in [9] and [14]. In [9], it was numerically demonstrated that an iterative blocking-based MLE yields lower MSE than the blocking-based LS estimator proposed in [2].…”

“…In the noisy case, quality assessment was discussed in [9] and [14]. In [9], it was numerically demonstrated that an iterative blocking-based MLE yields lower MSE than the blocking-based LS estimator proposed in [2]. In [14], closedform CRBs were derived for the two previously proposed MLEs of the reverberation PSD, namely the blocking-based estimator in [5] and the non-blocking-based estimator in [6].…”

“…An important benefit of considering the rank-deficient noise as a separated problem, is due to the form of the solution. In the ML framework, a closed-form solution exists for the noiseless case [1], [3] but not for the full-rank noise scenario, thus requiring iterative optimization techniques [5], [6], [9] (as opposed to LS method that has closed-form solutions in both cases). However, we show here that when the noise PSD trace of a matrix ⊗ Kronecker product vec(·) stacking the columns of a matrix on top of one another matrix is a rank-deficient matrix, closed-form MLE exists, which yields simpler and faster estimation procedure with low computational complexity, and is not sensitive to local maxima.…”

A multichannel diffuse power estimator for dereverberation in the presence of multiple sources

“…In [20], we proposed a method to estimate the diffuse sound PSD using multiple reference signals, while we assumed at most one active source at a known position. In [21], a direct maximum likelihood estimate of the diffuse sound PSD given the observed signals was derived by assuming a noise-free signal model and using prior knowledge of the source position and the diffuse coherence. As the estimator presented in [21] considers only one sound source and no additive noise, we do not consider the estimator in the present work.…”