Reverberation Power Spectral Density Research Articles

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

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, Cramer-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.

Scoring-Based ML Estimation and CRBs for Reverberation, Speech, and Noise PSDs in a Spatially Homogeneous Noise Field

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 Cramer-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.

Analysis of Eigenvalue Decomposition-Based Late Reverberation Power Spectral Density Estimation

Many speech dereverberation techniques require an estimate of the late reverberation power spectral density (PSD). State-of-the-art multichannel methods for estimating the late reverberation PSD typically rely on first, an estimate of the relative transfer functions (RTFs) of the target signal; second, a model for the spatial coherence matrix of the late reverberation; and finally, an estimate of the reverberant speech or reverberant and noisy speech PSD matrix. The RTFs, the spatial coherence matrix, and the speech PSD matrix are all prone to modeling and estimation errors in practice, with the RTFs being particularly difficult to estimate accurately, especially in highly reverberant and noisy scenarios. Recently, we proposed an eigenvalue decomposition (EVD)-based late reverberation PSD estimator, which does not require an estimate of the RTFs. In this paper, this EVD-based PSD estimator is further analyzed and its estimation accuracy and computational complexity are analytically compared to a state-of-the-art maximum likelihood (ML) based PSD estimator. It is shown that for perfect knowledge of the RTFs, spatial coherence matrix, and reverberant speech PSD matrix, the ML-based and the EVD-based PSD estimates are both equal to the true late reverberation PSD. In addition, it is shown that for erroneous RTFs but perfect knowledge of the spatial coherence matrix and reverberant speech PSD matrix, the ML-based PSD estimate is larger than or equal to the true late reverberation PSD, whereas the EVD-based PSD estimate is obviously still equal to the true late reverberation PSD. Finally, it is shown that when modeling and estimation errors occur in all quantities, the ML-based PSD estimate is larger than or equal to the EVD-based PSD estimate. Simulation results for several realistic acoustic scenarios demonstrate the advantages of using the EVD-based PSD estimator in a multichannel Wiener filter, yielding a significantly better performance than the ML-based PSD estimator.

Evaluation and Comparison of Late Reverberation Power Spectral Density Estimators

Reduction of late reverberation can be achieved using spatio-spectral filters, such as the multichannel Wiener filter. To compute this filter, an estimate of the late reverberation power spectral density (PSD) is required. In recent years, a multitude of late reverberation PSD estimators have been proposed. In this paper, these estimators are categorized into several classes, their relations and differences are discussed, and a comprehensive experimental comparison is provided. To compare their performance, simulations in controlled as well as practical scenarios are conducted. It is shown that a common weakness of spatial coherence-based estimators is their performance in high direct-to-diffuse ratio conditions. To mitigate this problem, a correction method is proposed and evaluated. It is shown that the proposed correction method can decrease the speech distortion without significantly affecting the reverberation reduction.

Cramér–Rao Bound Analysis of Reverberation Level Estimators for Dereverberation and Noise Reduction

The reverberation power spectral density (PSD) is often required for dereverberation and noise reduction algorithms. In this work, we compare two maximum likelihood (ML) estimators of the reverberation PSD in a noisy environment. In the first estimator, the direct path is first blocked. Then, the ML criterion for estimating the reverberation PSD is stated according to the probability density function of the blocking matrix (BM) outputs. In the second estimator, the speech component is not blocked. Instead, the ML criterion for estimating the speech and reverberation PSD is stated according to the probability density function of the microphone signals. To compare the expected mean square error (MSE) between the two ML estimators of the reverberation PSD, the Cramer–Rao Bounds (CRBs) for the two ML estimators are derived. We show that the CRB for the joint reverberation and speech PSD estimator is lower than the CRB for estimating the reverberation PSD from the BM outputs. Experimental results show that the MSE of the two estimators indeed obeys the CRB curves. Experimental results of multimicrophone dereverberation and noise reduction algorithm show the benefits of using the ML estimators in comparison with another baseline estimators.

Front-end technologies for robust ASR in reverberant environments—spectral enhancement-based dereverberation and auditory modulation filterbank features

This paper presents extended techniques aiming at the improvement of automatic speech recognition (ASR) in single-channel scenarios in the context of the REVERB (REverberant Voice Enhancement and Recognition Benchmark) challenge. The focus is laid on the development and analysis of ASR front-end technologies covering speech enhancement and feature extraction. Speech enhancement is performed using a joint noise reduction and dereverberation system in the spectral domain based on estimates of the noise and late reverberation power spectral densities (PSDs). To obtain reliable estimates of the PSDs—even in acoustic conditions with positive direct-to-reverberation energy ratios (DRRs)—we adopt the statistical model of the room impulse response explicitly incorporating DRRs, as well in combination with a novel proposed joint estimator for the reverberation time T 60 and the DRR. The feature extraction approach is inspired by processing strategies of the auditory system, where an amplitude modulation filterbank is applied to extract the temporal modulation information. These techniques were shown to improve the REVERB baseline in our previous work. Here, we investigate if similar improvements are obtained when using a state-of-the-art ASR framework, and to what extent the results depend on the specific architecture of the back-end. Apart from conventional Gaussian mixture model (GMM)-hidden Markov model (HMM) back-ends, we consider subspace GMM (SGMM)-HMMs as well as deep neural networks in a hybrid system. The speech enhancement algorithm is found to be helpful in almost all conditions, with the exception of deep learning systems in matched training-test conditions. The auditory feature type improves the baseline for all system architectures. The relative word error rate reduction achieved by combining our front-end techniques with current back-ends is 52.7% on average with the REVERB evaluation test set compared to our original REVERB result.