Non-stationary Noise Conditions Research Articles

Adaptive horizon size moving horizon estimation with unknown noise statistical properties

Abstract Moving horizon estimation (MHE) is an effective technique for state estimation. It formulates state estimation as an optimization problem over a finite time interval and is characterized by inherent robustness, flexibility, and explicit constraint handling capabilities. The horizon size is a crucial parameter influencing the estimation performance of MHE. However, the selection of the horizon size remains an open research question in the field of MHE. In this paper, we propose a novel adaptive horizon size MHE strategy that dynamically adjusts the horizon size based on the value of the objective function. This approach aims to improve the state estimation performance of MHE in real-time applications. Unlike conventional MHE methods that rely on a fixed horizon size, our adaptive strategy enhances robustness against unknown noise statistics by adjusting the horizon size. We analyze the convergence property of the estimation error and provide guidelines for parameter design to ensure optimal performance. The effectiveness and superiority of the proposed method are demonstrated through simulations involving an oscillatory system and a target tracking application under non-stationary noise conditions.

Robustness and sensitivity metrics-based tuning of the augmented Kalman filter for single-channel speech enhancement

The inaccurate estimates of the speech and noise linear prediction coefficients (LPCs) introduce bias in augmented Kalman filter (AKF) gain, which impacts the quality and intelligibility of enhanced speech. Although current tuning methods offset the bias in AKF gain, particularly in colored noise conditions, they do not adequately address nonstationary noise conditions. This paper introduces a new tuning algorithm of the AKF gain for speech enhancement in real-life noise conditions. Due to this purpose, a speech presence probability (SPP) method first estimates the noise power spectral density (PSD) from each noisy speech frame to compute the noise LPC parameters. A whitening filter is constructed with the noise LPCs to pre-whiten each noisy speech frame prior to computing the speech LPC parameters. The AKF is then constructed with the estimated speech and noise LPC parameters. To achieve better noise reduction, the robustness metric is employed to dynamically offset the bias in AKF gain during speech absence of the noisy speech to that of the sensitivity metric during speech presence. The speech activity is obtained through adopting the speech and noise production model parameters. It is shown that the reduced-biased AKF gain achieved by the proposed tuning algorithm addresses speech enhancement in real-life noise conditions. Objective and subjective scores on the NOIZEUS corpus demonstrate that the proposed method produces enhanced speech with higher quality and intelligibility than the competing methods in real-life noise conditions for a wide range of signal-to-noise ratio (SNR) levels.

A noise PSD estimation algorithm using derivative-based high-pass filter in non-stationary noise conditions

The minimum mean-square error (MMSE)-based noise PSD estimators have been used widely for speech enhancement. However, the MMSE noise PSD estimators assume that the noise signal changes at a slower rate than the speech signal— which lacks the ability to track the highly non-stationary noise sources. Moreover, the performance of the MMSE-based noise PSD estimator largely depends upon the accuracy of the a priori SNR estimation in practice. In this paper, we introduce a noise PSD estimation algorithm using a derivative-based high-pass filter in non-stationary noise conditions. The proposed method processes the silent and speech frames of the noisy speech differently to estimate the noise PSD. It is due to the non-stationary noise that can be mixed with silent and speech-dominated frames non-uniformly. We first introduce a spectral-flatness-based adaptive thresholding technique to detect the speech activity of the noisy speech frames. Since the silent frame of the noisy speech is completely filled with noise, the noise periodogram is directly computed from it without applying any filtering. Conversely, a 4th order derivative-based high-pass filter is applied during speech activity of the noisy speech frame to filter out the clean speech components while leaving behind mostly the noise. The noise periodogram is computed from the filtered signal—which counteracts the leaking of clean speech power. The noise PSD estimate is obtained by recursively averaging the previously estimated noise PSD and the current estimate of the noise periodogram. The proposed method is found to be effective in tracking the rapidly changing as well as the slowly varying noise PSD than the competing methods in non-stationary noise conditions for a wide range of signal-to-noise ratio (SNR) levels. Extensive objective and subjective scores on the NOIZEUS corpus demonstrate that the application of the proposed noise PSD with MMSE-based speech enhancement methods produce higher quality and intelligible enhanced speech than the competing methods.

Structural health monitoring with non-linear sensor measurements robust to unknown non-stationary input forcing

Bayesian filtering based structural health monitoring algorithms typically assume stationary white Gaussian noise models to represent an unknown input forcing. However, typical structural damages occur mostly under the action of extreme loading conditions, like earthquake or high wind/waves, which are characteristically non-stationary and non-Gaussian. Clearly, this invalidates this basic assumption, causing these algorithms to perform poorly under non-stationary noise conditions. This paper extends an existing interacting filtering algorithm to efficiently estimate structural damages while being robust to unknown non-stationary non-Gaussian input forcing. Furthermore, this approach is generalized beyond linear measurements to encompass the case of non-linear measurements such as strains. The joint estimation of state and parameters is performed by combining Ensemble Kalman filtering, for non-linear system state estimation, and Particle filtering to estimate changes in the structural parameters. The robustness against input forcing is achieved through an output injection approach embedded in the state filter equation. Numerical simulations for two kinds of response measurements (acceleration and strain) are performed on a 3D frame structure under different damage location and severity scenarios. The sensitivity with respect to noise and the impact of different sensor combinations have also been investigated.

Speech enhancement by LSTM-based noise suppression followed by CNN-based speech restoration

Single-channel speech enhancement in highly non-stationary noise conditions is a very challenging task, especially when interfering speech is included in the noise. Deep learning-based approaches have notably improved the performance of speech enhancement algorithms under such conditions, but still introduce speech distortions if strong noise suppression shall be achieved. We propose to address this problem by using a two-stage approach, first performing noise suppression and subsequently restoring natural sounding speech, using specifically chosen neural network topologies and loss functions for each task. A mask-based long short-term memory (LSTM) network is employed for noise suppression and speech restoration is performed via spectral mapping with a convolutional encoder-decoder network (CED). The proposed method improves speech quality (PESQ) over state-of-the-art single-stage methods by about 0.1 points for unseen highly non-stationary noise types including interfering speech. Furthermore, it is able to increase intelligibility in low-SNR conditions and consistently outperforms all reference methods.

Performance analysis of neural network, NMF and statistical approaches for speech enhancement

Bayesian Estimators are very useful in speech enhancement and noise reduction. But, it is noted that the traditional estimators process only amplitudes and the phase is left unprocessed. Among the Bayesian estimators, Super- Gaussian based estimators provide improved noise reduction. Super-Gaussian Bayesian estimators, which uses processed phase information for estimation of amplitudes provides further improved results. In this work, the Complex speech coefficients given Uncertain Phase (CUP) based Bayesian estimators like CUP-GG (CUP Estimator with speech spectral coefficients assumed as Gamma and noise spectral coefficients as Generalized Gamma), CUP-NG (Speech as Nakagami) are compared under white noise, pink noise, Babble noise and Non-Stationary factory noise conditions. The statistical estimators show less effective results under completely non-stationary assumptions like non-stationary factory noise, babble noise etc. Non-negative Matrix Factorization (NMF) based algorithms show better performance for non stationary noises. The drawback of NMF is, it requires apriori knowledge about speech. This drawback can be overcome by taking the advantages of both statistical approaches and NMF approaches. NR-NMF and WR-NMF speech enhancement methods are developed by providing posteriori regularization based on statistical assumption of speech and noise DFT coefficients distribution. Also a speech enhancement method which uses CUP-GG estimator and NMF with online noise bases update are considered for comparison. The progress in neural network based approaches for speech enhancement further shown that with large dataset and better training, the speech enhancement algorithms results in improved results. In this work, the neural network approach for speech enhancement is implemented and compared the method with traditional estimators and NMF approaches. For generalization of unseen noise types the proposed neural network approach uses dropout. Also for training the network, the features obtained from apriori SNR and aposteriori SNR is used in this method. The objective of this paper is to analyze the performance of speech enhancement methods based on Neural Network, NMF and statistical based. The objective performance measures Perceptual Evaluation of Speech Quality (PESQ), Short-Time Objective Intelligibility (STOI), Signal to Noise Ratio (SNR), Segmental SNR (Seg SNR) are considered for comparison.

GEDI: Gammachirp envelope distortion index for predicting intelligibility of enhanced speech

In this study, we propose a new concept, the gammachirp envelope distortion index (GEDI), based on the signal-to-distortion ratio in the auditory envelope, SDRenv, to predict the intelligibility of speech enhanced by nonlinear algorithms. The objective of GEDI is to calculate the distortion between enhanced and clean-speech representations in the domain of a temporal envelope extracted by the gammachirp auditory filterbank and modulation filterbank. We also extend GEDI with multi-resolution analysis (mr-GEDI) to predict the speech intelligibility of sounds under non-stationary noise conditions. We evaluate GEDI in terms of the speech intelligibility predictions of speech sounds enhanced by a classic spectral subtraction and a Wiener filtering method. The predictions are compared with human results for various signal-to-noise ratio conditions with additive pink and babble noises. The results showed that mr-GEDI predicted the intelligibility curves better than short-time objective intelligibility (STOI) measure, extended-STOI (ESTOI) measure, and hearing-aid speech perception index (HASPI) under pink-noise conditions, and better than HASPI under babble-noise conditions. The mr-GEDI method does not present an overestimation tendency and is considered a more conservative approach than STOI and ESTOI. Therefore, the evaluation with mr-GEDI may provide additional information in the development of speech enhancement algorithms.

Performance Improvement of Adaptive Wavelet Thresholding for Speech Enhancement Using Generalized Gaussian Priors and Frame-Wise Context Modeling

This work aims at developing an adaptive wavelet thresholding algorithm for speech enhancement with significant performance improvement over other wavelet-based counterparts. This is accomplished through the formulation of the optimum threshold for noise reduction, based on the generalized Gaussian priors to fully characterize the statistics of speech and noise wavelet coefficients. In addition, through the frame-wise context modeling which enables tracking of the statistical characteristics of each individual coefficient on the frame-wise basis, the optimum threshold is accurate and adaptive at both the coefficient level and frame level. The frame-wise context model is formulated by virtue of the context subspace projection of the wavelet coefficients, with the context index employed as the invariant correspondence between successive frame parameters, thereby enabling the frame-wise tracking at the coefficient level. Simulation results show significant improvement over the wavelet-based speech enhancement algorithms in terms of the segmental signal-to-noise ratio improvement by as much as 226%, the perceptual evaluation of speech quality by 36%, the short-time objective intelligibility by 17.8% and the cepstral distance by 33.3%. When benchmarked with the well-established short-time-Fourier-transform-based counterparts, the proposed wavelet thresholding algorithm offers favorable and more robust performances, particularly under non-stationary noise conditions, with no adverse musical noise effect.

Multi-Level Single-Channel Speech Enhancement Using a Unified Framework for Estimating Magnitude and Phase Spectra

Speech enhancement algorithms aim to improve the quality and intelligibility of noise corrupted speech, through spectral or temporal modifications. Most of the existing speech enhancement algorithms achieve this by modifying the magnitude spectrum alone, while keeping the phase spectrum intact. In the current work, both phase and magnitude spectra are modified to enhance noisy speech using a multi-level speech enhancement technique. Proposed phase compensation (PC) function achieves first-level enhancement by modifying the phase spectrum alone. Second-level enhancement performs energy redistribution in the phase compensated speech signal to make weak speech and non-speech regions highly contrastive. Energy redistribution from the energy-rich voiced to the weak unvoiced regions is carried out using adaptive power law transformation (APLT) technique by optimizing the parameters with a total energy constraint employing particle swarm optimization algorithm. Log MMSE technique with a novel speech presence uncertainty (SPU) estimation method is proposed for third-level enhancement. The compensated phase spectrum and the magnitude spectrum estimated using log MMSE, with proposed SPU estimation (log MMSE + proposed SPU), are used to reconstruct the enhanced speech signal. The proposed speech enhancement technique is compared with recent speech enhancement techniques that estimate both magnitude and phase, for various noise levels (−5 to +5 dB), in terms of objective and subjective measures. It is observed that the proposed technique improves signal quality and maintains or improves intelligibility under stationary, and non-stationary noise conditions.

Perceptual and Objective Assessment of Envelope Enhancement for Children With Auditory Processing Disorder.

This paper evaluated the performance of an envelope enhancement (EE) algorithm subjectively by children with auditory processing disorder (APD), and objectively through computational models. Speech intelligibility data was collected from children with APD, for unprocessed and envelope-enhanced speech in the presence of stationary and non-stationary background noise at different signal to noise ratios (SNRs), both with and without noise reduction (NR) algorithms as a front-end to the EE algorithm. Furthermore, intrusive and non-intrusive objective speech intelligibility metrics were derived to predict the perceptual impact of this EE algorithm. Subjective data for stationary noise conditions revealed that the combination of NR and EE algorithms significantly improved the speech intelligibility scores at poor SNRs. In contrast, the same combination was ineffective in improving speech intelligibility in non-stationary noise conditions. Taken together, subjective results suggest that exaggerating the envelope cues improves speech identification scores for children with APD. However, the benefit obtained varies depending upon the type and level of the background noise. Both intrusive and non-intrusive objective speech intelligibility estimators exhibited good correlation with the subjective data, with the intrusive metric demonstrating better generalization capabilities. Implications of these results for hearing aid applications for children with APD is discussed.

An Iterative Kalman Filter with Reduced-Biased Kalman Gain for Single Channel Speech Enhancement in Non-stationary Noise Condition

This paper presents an iterative Kalman filter (IT-KF) with a reduced-biased Kalman gain for single channel speech enhancement in Non-stationary Noise Conditions (NNCs). The proposed IT-KF aims to offset the bias in Kalman gain through efficient parameter estimation leading to improve the speech enhancement performance. To do this, we introduce a Decision Directed (DD) and a posteriori SNR based noise variance estimation method controlled through Speech Activity Detector (SAD). The proposed SAD incorporates a majority voting of three distinct SAD fusions. The LPC parameters are computed from the pre-smoothing of noisy speech. With these initial estimated parameters, an IT-KF processes the noisy speech at first iteration. The parameters are re-estimated from the processed speech, re-adjust the Kalman gain, and the process is repeated at second iteration. It is shown that the adjusted Kalman gain enables the IT-KF to minimize the remaining artifacts of the processed speech, yielding the enhanced speech. Extensive simulation results reveal that the proposed method outperforms other benchmark methods in NNCs for a wide range of SNRs.

Enhanced Speech Based Jointly Statistical Probability Distribution Function for Voice Activity Detection

Most of Voice activity detection (VAD) methods are based on statistical model. In these methods, the noise signal is always assumed to satisfy and characterized by Gaussian distribution, while the assumption of noise does not always hold in practice and which causes that these kinds of method fail to distinguish speech from noise at low Signal-noise-ratio (SNR) level in non-stationary noise condition. For going further to improve the robustness of VAD, a enhanced speech based method is proposed. In the proposed method, the Laplacian distribution is used to model the remained noise since we find that the remained noise in enhanced speech satisfy Laplacian distribution; in addition, Gaussian mixture model is used to characterize the Discrete Fourier transform (DFT) coefficients of reconstructed speech in enhanced speech. Experimental results show that the proposed method performs better than the baseline method, especially in low SNR and non-stationary noise conditions.

Sparse Hidden Markov Models for Speech Enhancement in Non-Stationary Noise Environments

We propose a sparse hidden Markov model (HMM)-based single-channel speech enhancement method that models the speech and noise gains accurately in non-stationary noise environments. Autoregressive models are employed to describe the speech and noise in a unified framework and the speech and noise gains are modeled as random processes with memory. The likelihood criterion for finding the model parameters is augmented with an ${l_p}$ regularization term resulting in a sparse autoregressive HMM (SARHMM) system that encourages sparsity in the speech- and noise- modeling. In the SARHMM only a small number of HMM states contribute significantly to the model of each particular observed speech segment. As it eliminates ambiguity between noise and speech spectra, the sparsity of speech and noise modeling helps to improve the tracking of the changes of both spectral shapes and power levels of non-stationary noise. Using the modeled speech and noise SARHMMs, we first construct a noise estimator to estimate the noise power spectrum. Then, a Bayesian speech estimator is derived to obtain the enhanced speech signal. The subjective and objective test results indicate that the proposed speech enhancement scheme can achieve a larger segmental SNR improvement, a lower log-spectral distortion and a better speech quality in stationary noise conditions than state-of-the-art reference methods. The advantage of the new method is largest for non-stationary noise conditions .

A wavelet-based thresholding approach to reconstructing unreliable spectrogram components

Data imputation approaches for robust automatic speech recognition reconstruct noise corrupted spectral information by exploiting prior knowledge of the relationship between target speech and background through the use of spectrographic masks. Most of these approaches are model-based techniques that can only provide accurate estimates of the underlying clean speech when the characteristics of the noise corrupted features do not deviate from those of the model. Discrete wavelet transform (DWT) based de-noising methods can also be used for re-estimating the underlying clean speech from a noise corrupted signal, but often require that the background noise is stationary and modeled by a Gaussian distribution. A novel approach is presented here for incorporating the information derived from spectrographic masks in a DWT-based de-noising method. The spectrographic masks are used for deriving thresholds for de-noising wavelet domain coefficients making DWT based de-noising more suitable for non-stationary noise conditions. The results of an experimental study are presented to demonstrate the performance of DWT based data imputation relative to other established techniques on the Aurora 2 noisy speech recognition task. It will be shown that the proposed approach reduces the impact of model mismatch associated with parametric approaches and exploits the robustness of non-parametric wavelet de-noising approach.

On speech features fusion, α-integration Gaussian modeling and multi-style training for noise robust speaker classification

This paper investigates the fusion of Mel-frequency cepstral coefficients (MFCC) and statistical pH features to improve the performance of speaker verification (SV) in non-stationary noise conditions. The <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$\alpha $</tex></formula> -integrated Gaussian Mixture Model ( <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\alpha $</tex></formula> -GMM) classifier is adopted for speaker modeling. Two different approaches are applied to reduce the effects of noise corruption in the SV task: speech enhancement and multi-style training (MT). The spectral subtraction with minimum statistics (MS/SS) and the optimally-modified log-spectral amplitude with improved minima controlled recursive averaging (IMCRA/OMLSA) are examined for the speech enhancement procedure. The MT techniques are based on colored (Colored-MT), white (White-MT) and narrow-band (Narrow-MT) noises. Six real non-stationary noises, collected from different acoustic sources, are used to corrupt the TIMIT speech database in four different signal-to-noise ratios (SNR). The index of non-stationarity (INS) is chosen for the stationarity tests of the acoustic noises. Complementary SV experiments are conducted in realistic noisy conditions using the MIT database. The results show that the best SV accuracy was obtained with the MFCC + pH features fusion, the MS/SS and the Colored-MT.

Autocorrelation Analysis in Time and Frequency Domains for Passive Structural Diagnostics

In this paper, modal frequency estimation by using autocorrelation functions in both the time and frequency domains for structural diagnostics is discussed. With popular structural health monitoring methods for periodic inspections such as with the “hammering test,” hearing is very useful for distinguishing differences between structural conditions. Hearing detects pitch and tone, and it is known that the auditory process is related to wave periodicity calculated from autocorrelation functions. Consequently, on the basis of the hammering test, modal frequencies can be estimated by autocorrelation, the same as hearing. In this paper, modal frequencies were estimated by using autocorrelation for constant structural health monitoring under a nonstationary noise condition. First, fundamental modal frequencies were estimated by using the autocorrelation of the time domain which was inspired by pitch detection of hearing. Second, higher modal frequency compositions were also analyzed by using autocorrelation in the frequency domain as with tones discrimination. From the results by conducting scale-model experiments under unknown nonstationary noise conditions, periods of fundamental modal frequency were derived by using periods histogram of autocorrelation functions. In addition, higher modal frequency estimation under nonstationary noises was also discussed.

Structural Vibration Monitoring Using Cumulative Spectral Analysis

This paper describes a resonance decay estimation for structural health monitoring in the presence of nonstationary vibrations. In structural health monitoring, the structure's frequency response and resonant decay characteristics are very important for understanding how the structure changes. Cumulative spectral analysis (CSA) estimates the frequency decay by using the impulse response. However, measuring the impulse response of buildings is impractical due to the need to shake the building itself. In a previous study, we reported on system damping monitoring using cumulative harmonic analysis (CHA), which is based on CSA. The current study describes scale model experiments on estimating the hidden resonance decay under non-stationary noise conditions by using CSA for structural condition monitoring.

Speech enhancement using a structured codebook

Codebook-based speech enhancement methods that use trained codebooks of speech and noise spectra provide good performance even under non-stationary noise conditions. A drawback, however, is their high computational cost. For every pair of speech and noise codebook vectors, a likelihood score indicating how well that pair matches the observation is computed. In this paper, a method that identifies and performs only relevant likelihood computations by imposing a hierarchical structure on the speech codebook is proposed. The performance of the proposed method is shown to be close to that of the original scheme but at a significantly lower computational cost.

Evaluation of model-based versus non-parametric monaural noise-reduction approaches for hearing aids

Objective: Single channel noise reduction has been well investigated and seems to have reached its limits in terms of speech intelligibility improvement, however, the quality of such schemes can still be advanced. This study tests to what extent novel model-based processing schemes might improve performance in particular for non-stationary noise conditions. Design: Two prototype model-based algorithms, a speech-model-based, and a auditory-model-based algorithm were compared to a state-of-the-art non-parametric minimum statistics algorithm. A speech intelligibility test, preference rating, and listening effort scaling were performed. Additionally, three objective quality measures for the signal, background, and overall distortions were applied. For a better comparison of all algorithms, particular attention was given to the usage of the similar Wiener-based gain rule. Study sample: The perceptual investigation was performed with fourteen hearing-impaired subjects. Results: The results revealed that the non-parametric algorithm and the auditory model-based algorithm did not affect speech intelligibility, whereas the speech-model-based algorithm slightly decreased intelligibility. In terms of subjective quality, both model-based algorithms perform better than the unprocessed condition and the reference in particular for highly non-stationary noise environments. Conclusion: Data support the hypothesis that model-based algorithms are promising for improving performance in non-stationary noise conditions.

An Adaptive Wavelet-Based Denoising Algorithm for Enhancing Speech in Non-stationary Noise Environment

Traditional wavelet-based speech enhancement algorithms are ineffective in the presence of highly non-stationary noise because of the difficulties in the accurate estimation of the local noise spectrum. In this paper, a simple method of noise estimation employing the use of a voice activity detector is proposed. We can improve the output of a wavelet-based speech enhancement algorithm in the presence of random noise bursts according to the results of VAD decision. The noisy speech is first preprocessed using bark-scale wavelet packet decomposition (BSWPD) to convert a noisy signal into wavelet coefficients (WCs). It is found that the VAD using bark-scale spectral entropy, called as BS-Entropy, parameter is superior to other energy-based approach especially in variable noise-level. The wavelet coefficient threshold (WCT) of each subband is then temporally adjusted according to the result of VAD approach. In a speech-dominated frame, the speech is categorized into either a voiced frame or an unvoiced frame. A voiced frame possesses a strong tone-like spectrum in lower subbands, so that the WCs of lower-band must be reserved. On the contrary, the WCT tends to increase in lower-band if the speech is categorized as unvoiced. In a noise-dominated frame, the background noise can be almost completely removed by increasing the WCT. The objective and subjective experimental results are then used to evaluate the proposed system. The experiments show that this algorithm is valid on various noise conditions, especially for color noise and non-stationary noise conditions.