Hands-free speech systems are subject to performance degradation due to reverberation and noise. Common methods for enhancing reverberant and noisy speech require the knowledge of the speech, reverberation and noise power spectral densities (PSDs). Most literature on this topic assumes that the noise power spectral density (PSD) matrix is known. However, in many practical acoustic scenarios, the noise PSD is unknown and should be estimated along with the speech and the reverberation PSDs. In this article, the noise is modeled as a spatially homogeneous sound field, with an unknown time-varying PSD multiplied by a known time-invariant spatial coherence matrix. We derive two maximum likelihood estimators (MLEs) for the various PSDs, including the noise: The first is a non-blocking-based estimator, that jointly estimates the PSDs of the speech, reverberation and noise components. The second MLE is a blocking-based estimator, that blocks the speech signal and estimates the reverberation and noise PSDs. Since a closed-form solution does not exist, both estimators iteratively maximize the likelihood using the Fisher scoring method. In order to compare both methods, the corresponding Cramér-Rao Bounds (CRBs) are derived. For both the reverberation and the noise PSDs, it is shown that the non-blocking-based CRB is lower than the blocking-based CRB. Performance evaluation using both simulated and real reverberant and noisy signals, shows that the proposed estimators outperform competing estimators, and greatly reduce the effect of reverberation and noise.

Speech communication systems are prone to performance degradation in reverberant and noisy acoustic environments. Dereverberation and noise reduction algorithms typically require several model parameters, e.g. the speech, reverberation and noise power spectral densities (PSDs). A commonly used assumption is that the noise PSD matrix is known. However, in practical acoustic scenarios, the noise PSD matrix is unknown and should be estimated along with the speech and reverberation PSDs. In this article, we consider the case of rank-deficient noise PSD matrix, which arises when the noise signal consists of multiple directional noise sources, whose number is less than the number of microphones. We derive two closed-form maximum likelihood estimators (MLEs). The first is a non-blocking-based estimator which jointly estimates the speech, reverberation and noise PSDs, and the second is a blocking-based estimator, which first blocks the speech signal and then jointly estimates the reverberation and noise PSDs. Both estimators are analytically compared and analyzed, and mean square errors (MSEs) expressions are derived. Furthermore, Cramér-Rao Bounds (CRBs) on the estimated PSDs are derived. The proposed estimators are examined using both simulation and real reverberant and noisy signals, demonstrating the advantage of the proposed method compared to competing estimators.

We present a fully Bayesian hierarchical approach for multichannel speech enhancement with time-varying audio channel. Our probabilistic approach relies on a Gaussian prior for the speech signal and a Gamma hyperprior for the speech precision, combined with a multichannel linear-Gaussian state-space model for the acoustic channel. Furthermore, we assume a Wishart prior for the noise precision matrix. We derive a variational expectation-maximization (VEM) algorithm that uses a variant of a multichannel Wiener filter (MCWF) to infer the sound source and a Kalman smoother to infer the acoustic channel. It is further shown that the VEM speech estimator can be recasted as a multichannel minimum variance distortionless response (MVDR) beamformer followed by a single-channel variational postfilter. The proposed algorithm was evaluated using both simulated and real room environments with several noise types and reverberation levels. Both static and dynamic scenarios are considered. In terms of speech quality, it is shown that a significant improvement is obtained with respect to the noisy signal, and that the proposed method outperforms a baseline algorithm. In terms of channel alignment and tracking ability, a superior channel estimate is demonstrated.

This paper addresses the problem of blind adaptive beamforming using a hierarchical Bayesian model. Our probabilistic approach relies on a Gaussian prior for the speech signal and a Gamma hyperprior for the speech precision, combined with a multichannel linear-Gaussian state-space model for the possibly time-varying acoustic channel. Furthermore, we assume a Gamma prior for the ambient noise precision. We present a variational Expectation-Maximization (VEM) algorithm that employs a variant of multi-channel Wiener filter (MCWF) to estimate the sound source and a Kalman smoother to estimate the acoustic channel of the room. It is further shown that the VEM speech estimator can be decomposed into two stages: A multichannel minimum variance distortionless response (MVDR) beamformer and a subsequent single-channel variational postfilter. The proposed algorithm is evaluated in terms of speech quality, for a static scenario with recorded room impulse responses (RIRs). It is shown that a significant improvement is obtained with respect to the noisy signal, and that the proposed algorithm outperforms a baseline algorithm. In terms of channel alignment, a superior channel estimate is demonstrated compared to the causal Kalman filter.

We consider the transmission of a memoryless bivariate Gaussian source over a two-user additive Gaussian multiple-access channel with unidirectional conferencing encoders. Here, prior to each transmission block, Encoder 1, which observes the first source component, is allowed to communicate with Encoder 2, which observes the second source component, via a unidirectional noise-free bit-pipe of given capacity. The main results of this paper are sufficient conditions and a necessary condition for the achievability of a distortion pair expressed as a function of the channel SNR and of the source correlation. The main sufficient condition is obtained by an extension of the vector-quantizer scheme suggested by Lapidoth-Tinguely, for the case without conferencing, to the case with unidirectional conference. In the high-SNR regime, and when the capacity of the conference channel is unlimited, these necessary and sufficient conditions are shown to agree. We evaluate the precise high-SNR asymptotics for a subset of distortion pairs when the capacity of the conference channel is unlimited in which case we show that a separation-based scheme attains these optimal distortion pairs. However, with symmetric average-power constraints and fixed conferencing capacity, at high-SNR, the latter separation-based scheme is shown to be suboptimal.

We consider the transmission of a bivariate Gaussian memoryless source over a two-user additive Gaussian multiple-access channel with unidirectional conferencing. Here, prior to each transmission block Encoder 1 is allowed to communicate with Encoder 2 via a unidirectional noise-free bit-pipe of given capacity. We derive a necessary condition for the achievability of a distortion pair expressed as a function of the channel SNR and of the source correlation. In the high-SNR regime, and when the capacity of the conference channel is unlimited, the necessary condition is shown to agree with a sufficient condition derived previously by the authors. We evaluate the precise high-SNR asymptotics for a subset of distortion pairs when the conferencing capacity is unlimited in which case we show that the problem is separable.

We consider the problem of transmitting a bivariate Gaussian memoryless source over a two-user additive Gaussian multiple-access channel with unidirectional conferencing encoders. Here, prior to each transmission block Encoder 1 is allowed to communicate with Encoder 2 via a unidirectional noise-free bit-pipe of given capacity. We extend the vector-quantizer scheme suggested by Lapidoth-Tinguely, for the case without conferencing, to the case with unidirectional conference and derive an achievable rate-distortion region. We compare the performance of the suggested vector-quantizer to that of the optimal scheme for lossless transmission when the capacity of the conference link is large.