Noise Power Spectral Density Estimation Research Articles

An Analysis of Traditional Noise Power Spectral Density Estimators Based on the Gaussian Stochastic Volatility Model

Many single- and multi-channel speech enhancement techniques, old and new, rely in one way or another on estimates of the noise power spectral density (PSD). For example, the classical Wiener filter requires that either the speech or noise PSD be estimated. Typically, the noise PSD is estimated, as it is often easier to model and estimate than the speech. As a result, much attention has been paid to this important problem over the past couple of decades, with important scientific milestones being the minimum statistics (MS), the minima controlled recursive averaging (IMCRA), and the minimum mean squared (MMSE) estimators. Despite leading to major progress, these estimators are rather ad hoc, making them difficult to tune and improve in a systematic manner. In this article, we analyse some of the common heuristics employed in such noise PSD estimators to put them on firmer mathematical ground. More specifically, we use the Gaussian stochastic volatility model and show that the MMSE noise PSD estimator can be interpreted as a special case thereof. Moreover, we analyze the related problem of speech presence probability (SPP) estimation and show that the SPP estimation performed in the MMSE noise PSD estimator can be interpreted as an SNR estimator in the context of the Gaussian stochastic volatility model.

Rotor Noise-Aware Noise Covariance Matrix Estimation for Unmanned Aerial Vehicle Audition

A noise covariance matrix (NCM) estimation method for unmanned aerial vehicle (UAV) audition is proposed with rotor noise reduction as its primary focus. The proposed NCM estimation method could be incorporated into audio processing algorithms using UAV-mounted microphone array systems. The NCM is formed through accurate estimation of the microphone array input signal's amplitude and phase by using a multi-sensory rotor noise power spectral density (PSD) estimator and a filter formed by exploiting the acoustical relationship between the microphone array and the rotor noise sources, respectively. The estimated NCM aims to be readily incorporable into several source enhancement algorithms to reduce the effects of rotor noise and improve the resultant audio quality. Experiment evaluation using real in-flight UAV rotor noise recordings shows that the estimated NCM significantly improves rotor noise reduction (of up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\sim 28$</tex-math></inline-formula> dB) and the quality of the target sound.

Multi-sensory sound source enhancement for unmanned aerial vehicle recordings

A method to effectively perform sound source enhancement from an unmanned aerial vehicle (UAV)-mounted audio recording system is proposed. The objective of this study is to utilise audio recordings and non-acoustical UAV rotor characteristics to improve rotor noise power spectral density (PSD) estimation accuracy and robustness. The improved rotor noise PSD estimate in turn improves the effectiveness of the rotor noise postfilter, leading to improvement in source enhancement performance. The performance of the proposed source enhancement algorithm is evaluated via experiments, with recordings made in an outdoor environment with an in-flight UAV. Experiment results show PSD estimation accuracy to within 1.5 dB log spectral distortion regardless of the given input conditions, such as the presence of surrounding sound sources. The method also achieves a consistent ∼20–25 dB improvement in source enhancement performance, where the effects of rotor noise from the noisy microphone recordings are significantly reduced. The proposed method also outperforms existing state-of-the-art such as the beamformer with postfilter and speech distortion weighted multichannel Wiener filter frameworks.

Improved Speech Enhancement Considering Speech PSD Uncertainty

Speech enhancement based on statistical models has been studied for several decades. Recently, the speech enhancement adopting a speech power spectral density (PSD) uncertainty model has been proposed. This approach distinguishes the true speech PSD from its estimate and considers both as random variables. It incorporates a prior distribution of speech spectra and speech PSD estimators to derive the PSD uncertainty-aware counterpart to conventional clean speech estimators, which results in performance improvement. However, the speech PSD uncertainty model has not yet been adopted for parameter estimations such as <inline-formula><tex-math notation="LaTeX"><?TeX $\mathit{a posteriori}$?></tex-math></inline-formula> speech presence probability, noise PSD, and speech power spectra estimations in the speech enhancement framework. In this paper, we incorporate the speech PSD uncertainty model to all the components of the statistical model-based speech enhancement framework by deriving PSD uncertainty-aware counterparts to conventional parameter estimators. Specifically, we derive the <inline-formula><tex-math notation="LaTeX"><?TeX $\mathit{a posteriori}$?></tex-math></inline-formula> speech presence probability (SPP) where the likelihood function for each hypothesis is based on the speech PSD uncertainty. With this <inline-formula><tex-math notation="LaTeX"><?TeX $\mathit{a posteriori}$?></tex-math></inline-formula> SPP, a novel SPP-based noise PSD estimator is derived. Also, we derive the minimum mean-square error (MMSE) estimator for the power spectrum of the clean speech in the current frame under speech PSD uncertainty which is exploited to refine the speech PSD estimator. Finally, the refined speech PSD estimator is incorporated into the spectral gain function based on the speech PSD uncertainty model. The proposed approach showed improved noise PSD estimation performance in terms of the averaged logarithmic error distance, and improved speech enhancement performance in terms of the noise reduction, segmental signal-to-noise ratio, perceptual evaluation of speech quality (PESQ) scores and short-time objective intelligibility in our experiments. It also exhibited comparable performance with a real-time deep learning-based speech enhancement system in terms of the PESQ scores and composite measures for the VoiceBank-DEMAND dataset.

Low-complexity artificial noise suppression methods for deep learning-based speech enhancement algorithms

Deep learning-based speech enhancement algorithms have shown their powerful ability in removing both stationary and non-stationary noise components from noisy speech observations. But they often introduce artificial residual noise, especially when the training target does not contain the phase information, e.g., ideal ratio mask, or the clean speech magnitude and its variations. It is well-known that once the power of the residual noise components exceeds the noise masking threshold of the human auditory system, the perceptual speech quality may degrade. One intuitive way is to further suppress the residual noise components by a postprocessing scheme. However, the highly non-stationary nature of this kind of residual noise makes the noise power spectral density (PSD) estimation a challenging problem. To solve this problem, the paper proposes three strategies to estimate the noise PSD frame by frame, and then the residual noise can be removed effectively by applying a gain function based on the decision-directed approach. The objective measurement results show that the proposed postfiltering strategies outperform the conventional postfilter in terms of segmental signal-to-noise ratio (SNR) as well as speech quality improvement. Moreover, the AB subjective listening test shows that the preference percentages of the proposed strategies are over 60%.

Evaluation of speech enhancement algorithms applied to electrolaryngeal speech degraded by noise

Electrolaryngeal speech, for persons who have lost their larynx, suffers from the drawback of susceptibility to acoustic noise, which includes inherent electrolarynx motor noise as well as environmental noise. Interactions with electrolarynx users motivated the authors to investigate a crucial drawback of electrolaryngeal speech: degradation of electrolaryngeal speech under noisy environments. The effect of contemporary methods of speech enhancement, viz. noise power spectral density estimation based d-dimensional amplitude trimmed estimation (DATE), and non-negative matrix factorization (NMF) based algorithms, were studied and evaluated for electrolaryngeal speech degraded by noise. Electrolaryngeal speech was corrupted using three types of noisy scenarios at low signal to noise ratios (0, −5 and −10 dB SNR). Objective testing based on the perceptual evaluation of speech quality (PESQ) standard, as well as subjective testing by 14 participants based on the ITU-T P.835 standard were performed. Word-centric intelligibility testing was also performed. The results indicated an improvement in the speech quality. The subjective testing results were further analyzed using one-way analysis of variance (ANOVA) and multiple paired comparison using Tukey’s honest significant difference (HSD) criterion. The overall speech quality of NMF algorithms was found to be significantly higher than that of DATE-based algorithms for the test conditions. The results show that speech enhancement algorithms can aid in improving the electrolaryngeal user experience by reducing the effect of acoustic noise.

Gravitational-wave astronomy with an uncertain noise power spectral density

In order to extract information about the properties of compact binaries, we must estimate the noise power spectral density of gravitational-wave data, which depends on the properties of the gravitational-wave detector. In practice, it is not possible to know this perfectly, only to estimate it from the data. Multiple estimation methods are commonly used and each has a corresponding statistical uncertainty. However, this uncertainty is widely ignored when measuring the physical parameters describing compact binary coalescences, and the appropriate likelihoods which account for the uncertainty are not well known. In order to perform increasingly precise astrophysical inference and model selection, it will be essential to account for this uncertainty. In this work, we derive the correct likelihood for one of the most widely used estimation methods in gravitational-wave transient analysis, the median average. We demonstrate that simulated Gaussian noise follows the predicted distributions. We then examine real gravitational-wave data at and around the time of GW151012, a relatively low-significance binary black hole merger event. We show that the data are well described by stationary-Gaussian noise and explore the impact of different noise power spectral density estimation methods on the astrophysical inferences we draw about GW151012.

Optimum step-size control for a variable step-size stereo acoustic echo canceller in the frequency domain

The frequency-domain adaptive filter (FDAF) is a competitive candidate for stereo acoustic echo cancellation (SAEC) because of its good convergence and computational efficiency. However, there is a conflict between the convergence rate and the steady-state misalignment when using a constant step size. In this paper, a variable step-size approach is proposed for the stereo echo canceller in the frequency domain. The proposed method uses a first-order Markov model to describe the time-varying echo paths between the loudspeakers and the microphone. Following a statistical convergence analysis of the two-channel FDAF algorithm, the state recursion of the system distance in each frequency bin is given. The optimal step size is then derived by minimizing the system distance. Several practical problems, including noise power spectral density estimation and echo paths change detection, are discussed in details. Moreover, a close link between the proposed optimum step-size control method and the multichannel state–space frequency-domain adaptive filter is established. We show that the proposed variable step-size approach can also be incorporated into the block extended least-mean-square algorithm to fully exploit their benefits. Finally, computer simulations demonstrate that the proposed algorithm exhibits an excellent convergence performance and is very robust to the double talk.

DeepMMSE: A Deep Learning Approach to MMSE-Based Noise Power Spectral Density Estimation

An accurate noise power spectral density (PSD) tracker is an indispensable component of a single-channel speech enhancement system. Bayesian-motivated minimum mean-square error (MMSE)-based noise PSD estimators have been the most prominent in recent time. However, they lack the ability to track highly non-stationary noise sources due to current methods of a priori signal-to-noise (SNR) estimation. This is caused by the underlying assumption that the noise signal changes at a slower rate than the speech signal. As a result, MMSE-based noise PSD trackers exhibit a large tracking delay and produce noise PSD estimates that require bias compensation. Motivated by this, we propose an MMSE-based noise PSD tracker that employs a temporal convolutional network (TCN) a priori SNR estimator. The proposed noise PSD tracker, called DeepMMSE makes no assumptions about the characteristics of the noise or the speech, exhibits no tracking delay, and produces an accurate estimate that requires no bias correction. Our extensive experimental investigation shows that the proposed DeepMMSE method outperforms state-of-the-art noise PSD trackers and demonstrates the ability to track abrupt changes in the noise level. Furthermore, when employed in a speech enhancement framework, the proposed DeepMMSE method is able to outperform state-of-the-art noise PSD trackers, as well as multiple deep learning approaches to speech enhancement. Availability: DeepMMSE is available at: https://github.com/anicolson/DeepXi .

Microphone Array Wiener Post Filtering Using Monotone Operator Splitting

For array-based acoustic source enhancement, variants of multi-channel Wiener filters are commonly used. The approach includes a Wiener post-filter that requires the simultaneous estimation of the power spectral density (PSD) of the target source and of noise sources for each time-frame. Conventional methods generally do not exploit prior knowledge , such as sparsity of the source, in solving this simultaneous estimation problem. We show that, for common scenarios, the simultaneous PSD estimation with consideration of prior knowledge can be formulated as a convex optimization problem with linear constraints. We use monotone operator splitting (MOS) to solve the constrained optimization problem. Our experiments confirm that the proposed method improves the accuracy of the noise PSD estimation, and that the resulting enhanced target signal is of higher quality.

A novel fast nonstationary noise tracking approach based on MMSE spectral power estimator

Estimating the noise power spectral density (PSD) from the corrupted speech signal is an essential component for speech enhancement algorithms. In this paper, a novel noise PSD estimation algorithm based on minimum mean-square error (MMSE) is proposed. The noise PSD estimate is obtained by recursively smoothing the MMSE estimation of the current noise spectral power. For the noise spectral power estimation, a spectral weighting function is derived, which depends on the a priori signal-to-noise ratio (SNR). Since the speech spectral power is highly important for the a priori SNR estimate, this paper proposes an MMSE spectral power estimator incorporating speech presence uncertainty (SPU) for speech spectral power estimate to improve the a priori SNR estimate. Moreover, a bias correction factor is derived for speech spectral power estimation bias. Then, the estimated speech spectral power is used in “decision-directed” (DD) estimator of the a priori SNR to achieve fast noise tracking. Compared to three state-of-the-art approaches, i.e., minimum statistics (MS), MMSE-based approach, and speech presence probability (SPP)-based approach, it is clear from experimental results that the proposed algorithm exhibits more excellent noise tracking capability under various nonstationary noise environments and SNR conditions. When employed in a speech enhancement system, improved speech enhancement performances in terms of segmental SNR improvements (SSNR+) and perceptual evaluation of speech quality (PESQ) can be observed.

Bone-Conduction Sensor Assisted Noise Estimation for Improved Speech Enhancement.

State-of-the-art noise power spectral density (PSD) estimation techniques for speech enhancement utilize the so-called speech presence probability (SPP). However, in highly non-stationary environments, SPP-based techniques could still suffer from inaccurate estimation, leading to significant amount of residual noise or speech distortion. In this paper, we propose to improve speech enhancement by deploying the bone-conduction (BC) sensor, which is known to be relatively insensitive to the environmental noise compared to the regular air-conduction (AC) microphone. A strategy is suggested to utilized the BC sensor characteristics for assisting the AC microphone in better SPP-based noise estimation. To our knowledge, no previous work has incorporated the BC sensor in this noise estimation aspect. Consequently, the proposed strategy can possibly be combined with other BC sensor assisted speech enhancement techniques. We show the feasibility and potential of the proposed method for improving the enhanced speech quality by both objective and subjective tests.

Robust noise power spectral density estimation for binaural speech enhancement in time-varying diffuse noise field

In speech enhancement, noise power spectral density (PSD) estimation plays a key role in determining appropriate de-nosing gains. In this paper, we propose a robust noise PSD estimator for binaural speech enhancement in time-varying noise environments. First, it is shown that the noise PSD can be numerically obtained using an eigenvalue of the input covariance matrix. A simplified estimator is then derived through an approximation process, so that the noise PSD is expressed as a combination of the second eigenvalue of the input covariance matrix, the noise coherence, and the interaural phase difference (IPD) of the input signal. Later, to enhance the accuracy of the noise PSD estimate in time-varying noise environments, an eigenvalue compensation scheme is presented, in which two eigenvalues obtained in noise-dominant regions are combined using a weighting parameter based on the speech presence probability (SPP). Compared with the previous prediction filter-based approach, the proposed method requires neither causality delays nor explicit estimation of the prediction errors. Finally, the proposed noise PSD estimator is applied to a binaural speech enhancement system, and its performance is evaluated through computer simulations. The simulation results show that the proposed noise PSD estimator yields accurate noise PSD regardless of the direction of the target speech signal. Therefore, slightly better performance in quality and intelligibility can be obtained than that with conventional algorithms.

A novel regularization framework for transient noise reduction

In this paper, we propose a novel method for estimating clean speech from a single channel transient noise corrupted speech. In the proposed method we assume that speech spectrogram is both sparse and has temporal continuity property, and transient noise spectrogram is both sparse and has spectral continuity property. Based on these assumptions, we define a novel regularization model with sparsity and continuity imposing regularization terms for transient noise reduction. Then we solve the proposed model via alternating direction method of multipliers (ADMM) and derive an efficient iterative algorithm. Based on the assumption that transient noise spectrogram is low rank, we construct a binary mask that specifies locations of the transients and apply it in the proposed algorithm to achieve better separation results. Our method straightforwardly estimates speech and is free of noise power spectral density (PSD) estimation and does not need any pre-trained models of speech or noise. Experiments with various types of transient noises demonstrate effectiveness of the proposed method.

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.

잡음 파워 스펙트럼 밀도 추정을 이용한 서로소 배열과 프로퍼게이터 기법 기반의 향상된 도래각 추정 기법

잡음 파워 스펙트럼 밀도 추정을 이용한 서로소 배열과 프로퍼게이터 기법 기반의 향상된 도래각 추정 기법

Recent Developments in Speech Enhancement in the Short-Time Fourier Transform Domain

In this paper, we present an overview on the topic of noise reduction in the short-time Fourier transform (STFT) domain. First, we briefly review the conventional literature in the single- and multichannel cases separately. In the single-channel scenario, we focus on the spectral subtractive methods, Wiener filter based methods, speech amplitude estimators and estimators of the complex STFT coefficients. In the multi-channel scenario, we investigate in short a selection of key beamforming approaches as well as conventional post-filtering methods. Next, a detailed survey of the most recent advances in the STFT-based noise reduction methods is provided. This includes STSA estimators with super-Gaussian priors, noise power spectral density (PSD ) estimation, estimation methods in the modulation domain, estimation of spectral phase and noise PSD matrix estimation for multi-channel applications. Finally, we summarize the presented material and draw important conclusions on each of the investigated topics.

A Constrained MMSE LP Residual Estimator for Speech Dereverberation in Noisy Environments

After revealing that both late reverberation and noise are additive interference components in the residual domain, this paper proposes to suppress these additive interference components by using a constrained minimum mean square error linear prediction (LP) residual estimator, where the optimal filter can be obtained by the generalized singular value decomposition. We propose to estimate the LP residuals for both late reverberation and noise continuously, which is based on the non-VAD related noise power spectral density estimator and the incessant late reverberant spectral variance estimator. The non-intrusive objective measure and the PESQ show that the proposed algorithm is better than traditional LP residual-based algorithms and spectral subtraction-based algorithms.

An adaptive noise power spectral density estimation of noisy speech using generalized gamma probability density function

Estimation of the power spectral density (PSD) of noise is crucial for retrieving speech in a noisy environment. 3 novel methods for estimating the non-white noise PSD of noisy speech based on a generalized gamma distribution and 3 criterions are proposed, which are minimum mean square error (MMSE), maximum a posteriori (MAP) and Maximum likelihood estimation (MLE). Because of the highly non-stationary nature of speech, it is difficult to derive the real probability density function (PDF) using any modeling technique. On the other hand, segmental noise is more stationary and can be fitted more accurately by a generalized gamma PDF, which is a natural extension of the Gaussian modeling for the distribution of non-white components. The results show that non-white noise spectrum fit more accurately on the generalized gamma PDF with adaptive parameters than on a Gaussian distribution function. The reported generalized gamma PDF model shows the better performance in estimating noise PSD compared to minimum statistics, MMSE-based and MLE noise PSD estimation methods. The performance of the proposed noise estimation is good when it is integrated with the speech-enhancement technique, as demonstrated log error, segmental SNR and PESQ measures.

Transient Noise Reduction Using Nonlocal Diffusion Filters

Enhancement of speech signals for hands-free communication systems has attracted significant research efforts in the last few decades. Still, many aspects and applications remain open and require further research. One of the important open problems is the single-channel transient noise reduction. In this paper, we present a novel approach for transient noise reduction that relies on non-local (NL) neighborhood filters. In particular, we propose an algorithm for the enhancement of a speech signal contaminated by repeating transient noise events. We assume that the time duration of each reoccurring transient event is relatively short compared to speech phonemes and model the speech source as an auto-regressive (AR) process. The proposed algorithm consists of two stages. In the first stage, we estimate the power spectral density (PSD) of the transient noise by employing a NL neighborhood filter. In the second stage, we utilize the optimally modified log spectral amplitude (OM-LSA) estimator for denoising the speech using the noise PSD estimate from the first stage. Based on a statistical model for the measurements and diffusion interpretation of NL filtering, we obtain further insight into the algorithm behavior. In particular, for given transient noise, we determine whether estimation of the noise PSD is feasible using our approach, how to properly set the algorithm parameters, and what is the expected performance of the algorithm. Experimental study shows good results in enhancing speech signals contaminated by transient noise, such as typical household noises, construction sounds, keyboard typing, and metronome clacks.