Robert Rehr

Phase estimation in speech enhancement — Unimportant, important, or impossible?

In recent years, research in the field of single channel speech enhancement has focused on the enhancement of spectral amplitudes while the noisy spectral phase was left unchanged. In this paper we review the motivation for neglecting phase estimation in the past, and why recent publications imply that the estimation of the clean speech phase may be beneficial after all. Further, we present an algorithm for blindly estimating the clean speech spectral phase from the noisy observation and show that the application of this phase estimate improves the predicted speech quality.

On the bias of adaptive first-order recursive smoothing

In signal processing, first-order recursive smoothing is often used to determine the mean of a nonstationary random variable. In order to find a better compromise between the tracking speed and the variance of the estimate, adaptive smoothing factors have been proposed, e.g., for single-channel background noise power spectral density estimators. In this paper, the bias of recursive smoothing using adaptive smoothing functions is investigated. For adaptive functions that do not depend on the estimated mean an analytical derivation of the bias is given. For adaptive functions having a dependence on the recursively estimated mean, an iterative procedure is proposed which allows to approximately determine the bias with a sufficiently high precision.

On the Importance of Super-Gaussian Speech Priors for Machine-Learning Based Speech Enhancement

For enhancing noisy signals, machine-learning based single-channel speech enhancement schemes exploit prior knowledge about typical speech spectral structures. To ensure a good generalization and to meet requirements in terms of computational complexity and memory consumption, certain methods restrict themselves to learning speech spectral envelopes. We refer to these approaches as machine-learning spectral envelope (MLSE)-based approaches. In this paper, we show by means of theoretical and experimental analyses that for MLSE-based approaches, super-Gaussian priors allow for a reduction of noise between speech spectral harmonics which is not achievable using Gaussian estimators such as the Wiener filter. For the evaluation, we use a deep neural network based phoneme classifier and a low-rank nonnegative matrix factorization framework as examples of MLSE-based approaches. A listening experiment and instrumental measures confirm that while super-Gaussian priors yield only moderate improvements for classic enhancement schemes, for MLSE-based approaches super-Gaussian priors clearly make an important difference and significantly outperform Gaussian priors.

An Analysis of Adaptive Recursive Smoothing with Applications to Noise PSD Estimation

First-order recursive smoothing filters using a fixed smoothing constant are in general unbiased estimators of the mean of a random process. Due to their efficiency in terms of memory consumption and computational complexity, they are of high practical relevance and are also often used to track the first-order moment of nonstationary random processes. However, in single-channel speech-enhancement applications, e.g., for the estimation of the noise power spectral density, an adaptively changing smoothing factor is often employed. Here, the adaptivity is used to avoid speech leakage by raising the smoothing factor when speech is likely to be present. In this paper, we investigate the properties of adaptive first-order recursive smoothing factors applied to noise power spectral density estimators. We show that in contrast to a smoothing with fixed smoothing factors, adaptive smoothing is in general biased. We propose different methods to quantify and to compensate for the bias. We demonstrate that the proposed correction methods reduce the estimation error and increases the perceptual evaluation of speech quality scores in a speech enhancement framework.

BIAS correction methods for adaptive recursive smoothing with applications in noise PSD estimation

Due to the low computational complexity and the low memory consumption, first-order recursive smoothing is a technique often applied to estimate the mean of a random process. For instance, recursive smoothing is used in noise power estimators where adaptively changing smoothing factors are used instead of fixed ones to prevent the speech power from leaking into the noise estimate. However, in general, the usage of adaptive smoothing factors leads to a biased estimate of the mean. In this paper, we propose a novel method to correct the bias evoked by adaptive smoothing factors. We compare this method to a recently proposed compensation method in terms of the log-error distortion using real world signals for two noise power estimators. We show that both corrections reduce the distortion measure in noisy speech while the novel method has the advantage that no iteration is required for determining the correction factor.

Cepstral noise subtraction for robust automatic speech recognition

The robustness of speech recognizers towards noise can be increased by normalizing the statistical moments of the Mel-frequency cepstral coefficients (MFCCs), e. g. by using cepstral mean normalization (CMN) or cepstral mean and variance normalization (CMVN). The necessary statistics are estimated over a long time window and often, a complete utterance is chosen. Consequently, changes in the background noise can only be tracked to a limited extent which poses a restriction to the performance gain that can be achieved by these techniques. In contrast, algorithms recently developed for single-channel speech enhancement allow to track the background noise quickly. In this paper, we aim at combining speech enhancement techniques and feature normalization methods. For this, we propose to transform an estimate of the noise power spectral density to the MFCC domain, where we subtract it from the noisy MFCCs. This is followed by a conventional CMVN. For background noises that are too instationary for CMVN but can be tracked by the noise estimator, we show that this processing leads to an improvement in comparison to the sole application of CMVN. The observed performance gain emerges especially in low signal-to-noise-ratios.