Non-stationary Noise Research Articles

A Self-Supervised Denoising Method Based on Deep Noise Estimation

Seismic random noise attenuation is an essential procedure when processing seismic data. Due to various acquisition environments and complex geological conditions, random noise in seismic field data exhibits spatiotemporal levels, significantly increasing the difficulty of extracting seismic signals. The deep learning (DL) methods have shown excellent performances for seismic denoising. However, most existing discriminative DL methods cannot fit field data with noise levels and signal structures that differ from the training set. To tackle the unmatching challenge, we propose a self-supervised deep denoising model named noise estimation-based convolution neural network (NE-CNN), which contains a multiscale denoising module as a pretrained model and a dual-path noise estimation module that estimates the noise level of each data patch with a generalized Gaussian distribution and gray-level co-occurrence matrix (GLCM). With Stein’s unbiased risk estimate (SURE), we can fine-tune the pretrained denoising module according to the estimated noise levels in a self-supervised style solely on data to be processed, leading to a boost of robustness to nonstationary seismic noise. In synthetic and field data tests, NE-CNN performed satisfactorily compared with discriminative DL methods in denoising effects on seismic data with nonstationary noise.

Magnetic Anomaly Detection Based on Energy-Concentrated Discrete Cosine Wavelet Transform

The magnetic anomaly signal tends to be contaminated by ambient environmental noise due to the complexity and diversity in the field of magnetic anomaly detection (MAD). The current denoising methods are effective in improving the signal-to-noise ratio (SNR). However, most of them are only applicable to the Gaussian noise and perform poorly for the practical geomagnetic noise, that is the nonstationary noise with a power spectral density (PSD) of 1/ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f^a</i> . To solve this issue, a MAD method based on energy concentrated discrete cosine wavelet transform is proposed in this paper. A novel framework through fusing wavelet transform and discrete cosine transform, dubbed WT-DCT, is constructed, which consists of abnormal signal acquisition, frequency domain energy concentration, and discrete wavelet transformation. The SNR of the magnetic anomaly is improved by extracting the principal components of the scale signal in wavelet transformation through the discrete cosine transform. Through comparing the WT-DCT to four commonly used and accepted methods with extensive simulations and field tests, the results demonstrate that with variations of the geomagnetic noise strengths in the range from 250 nT to 1000 nT, the proposed WT-DCT achieves the highest SNR improvement by about 44.81% and the best structural similarity (SSIM) improvement by about 84.75%.

Robust Cubature Kalman Filter With Gaussian-Multivariate Laplacian Mixture Distribution and Partial Variational Bayesian Method

This paper explores the problem of nonlinear state estimation in the presence of outlier-contaminated measurements. First, to deal with the non-stationary non-Gaussian noises caused by randomly occurring measurement outliers, we propose a new Gaussian-multivariate Laplacian mixture (GMLM) distribution and construct it as a hierarchical Gaussian expression. Next, utilizing the GMLM distribution and existing variational Bayesian (VB) method, a robust cubature Kalman filter is derived (VB-GMLMRCKF). Then, considering the high computational complexity of the existing VB inference process, a new partial VB (PVB) method is developed, which can separately estimate state vector and mismatched measurement noise covariance matrix. Building upon the VB-GMLMRCKF and PVB approach, a novel robust cubature Kalman filter is derived (PVB-GMLMRCKF). Finally, a target tracking model is utilized to evaluate the PVB-GMLMRCKF in terms of estimation accuracy, estimation consistency and computational efficiency.

Spatiotemporal Processing for Remote Sensing of Trapped Victims Using 4-D Imaging Radar

It is of great importance to remotely sense trapped victims with radio signals in modern search and rescue after natural disasters like earthquakes, avalanches, building collapses, and so on. Various radio sensors have been developed to date; however, they are hardly deployed to recognize efficiently the vital sign in long-distance, deep-coverage, and multi-subject situations because the back-scattered victim-critical radio signals are really weak and are nearly drowned in the ambient nonstationary noise and clutter. To tackle the formidable difficulty, we present a four-dimensional wideband microwave radar operating at 1.7 GHz to 2.7 GHz and develop a spatio-temporal processing algorithm to fully explore the vital knowledge of victims in the three-dimensional spatial and one-dimensional temporal information. We conducted comprehensive field experiments in real post-disaster environments and demonstrated experimentally that our radio sensor can continuously monitor multiple survivors trapped under mounds of debris in real urban environments. Moreover, we demonstrate that the presented method can achieve a signal-to-noise-and-clutter ratio improvement of more than 20 dB even in the case of deep burial, which enables localizing the victims trapped in the order of ten meters and recognizing the survivors’ vital states. We expect that the presented strategy may open an avenue for future remote life-rescuing and beyond in practical applications.

A Digital CCD Noise Reduction Technique Experimentally Tested on a Large Batch of Scientific Sensors

In this paper, a digital optimal-filtering method is proposed for reducing readout noise in charge-coupled devices (CCDs). The technique includes a number of noise sources that other methods omit but may restrict the sensor’s effectiveness. A procedure is described to obtain the noise directly from the video signal under standard readout sequence, instead of using an indirect noise measurements approach that do not capture all the interference sources. The proposed research method underwent extensive experimental testing on a large number of scientific sensors, reducing noise in comparison to standard techniques. A significant improvement in the performance comes from using a non-stationary noise model for the video signal and the calibration of the dynamics of the charge transfer signal for each sensor. The average reduction in the noise standard deviation of all tested devices was approximately 40%. Moreover, the spread of the standard deviation values was reduced compared to the standard technique. These two aspects indicate that this technique may increase the selection yield for the construction of multiple-sensors instruments.

Noise Reduction Based on Adaptive Prediction Fitting Algorithm for a Heterodyne Φ-OTDR System

Aiming to reduce the noise better in distributed optical fiber vibration sensing system, an adaptive predictive filtering algorithm is proposed to improve the overall signal-to-noise ratio (SNR) of vibration detection. A phase-sensitive optical time domain reflectometric ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Phi $ </tex-math></inline-formula> -OTDR) system based on heterodyne detection with dual AOMs is designed to reduce the requirement of DAQ high sampling rate, and an adaptive prediction noise reduction method based on normalized least mean square (NLMS) is adopted to reduce the non-stationary noise. Experimental results show that the SNR is increased from 8.14dB to 22.31dB. Compared with moving difference average method, wavelet denoising method and Prewitt edge detection method, the SNR of the adaptive prediction noise reduction algorithm is the highest, which would have potential application in disturbance detection under a strong noise environment.

Real-time noise cancellation with deep learning.

Biological measurements are often contaminated with large amounts of non-stationary noise which require effective noise reduction techniques. We present a new real-time deep learning algorithm which produces adaptively a signal opposing the noise so that destructive interference occurs. As a proof of concept, we demonstrate the algorithm's performance by reducing electromyogram noise in electroencephalograms with the usage of a custom, flexible, 3D-printed, compound electrode. With this setup, an average of 4dB and a maximum of 10dB improvement of the signal-to-noise ratio of the EEG was achieved by removing wide band muscle noise. This concept has the potential to not only adaptively improve the signal-to-noise ratio of EEG but can be applied to a wide range of biological, industrial and consumer applications such as industrial sensing or noise cancelling headphones.

Digital Control and Readout of MEMS Gyroscope Using Second-Order Sliding Mode Control

Microelectromechanical system (MEMS) is a kind of MEMS that has been utilized to monitor the angular speed of moving objects on several occasions and has attracted the interest of several organizations across the globe. This type of sensor has the benefits of excellent integration, cheap cost, and low power utilization. This study begins by describing the research and development of silicon MEMS gyroscopes since the 1980s, including the work of several universities, such as Draper Laboratory and UC Berkeley, as well as various design ideas, control systems, and architectures. Matching resonance frequencies of the driving and sense mechanical resonators may significantly improve the efficiency of MEMS gyroscopes. In a closed-loop readout circuit, however, exact control of the resonance frequency is difficult. Because of their inexpensive production costs in large numbers, MEMS gyroscopes are gaining appeal. Because of substantial nonstationary noise processes in the output of MEMS gyros, such as 1/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${f}$ </tex-math></inline-formula> noise, this creates difficulty for navigation system designing. In the implementation, relative error in ramp and step function is determined through the proposed methodology. Furthermore, the second-order sliding mode control (SoSMC) is used in the sliding mode of the gyroscope to minimize the chattering effect.

Block-Adaptive Rényi Entropy-Based Denoising for Non-Stationary Signals.

This paper approaches the problem of signal denoising in time-variable noise conditions. Non-stationary noise results in variable degradation of the signal's useful information content over time. In order to maximize the correct recovery of the useful part of the signal, this paper proposes a denoising method that uses a criterion based on amplitude segmentation and local Rényi entropy estimation which are limited over short time blocks of the signal spectrogram. Local estimation of the signal features reduces the denoising problem to the stationary noise case. Results, presented for synthetic and real data, show consistently better performance gained by the proposed adaptive method compared to denoising driven by global criteria.

ECG enhancement using a modified Bayesian framework and particle swarm optimization

Extended Kalman filter (EKF) is a well-known nonlinear Bayesian framework deployed in various electrocardiogram (ECG) processing applications. However, it is not very effective in removing non-stationary noises, such as muscle artifacts (MA) that are common in ECG recordings. As a model-based framework, this filter relies on its predefined state space model. As a result, EKF fails when ECG dynamics don’t comply its state-space model. In order to solve the above issues, in this paper, we propose to use particle swarm optimization (PSO) to find a better and more accurate state-space model. In addition, in order to improve EKF performance in nonstationary environments, we propose a new measurement model. This Model is modified to include non-Gaussian non-stationary additive and stationary noises. However, in order for EKF to use this model, its equations should be reformulated. Two different approaches are proposed in this paper to reformulate EKF equations; 1-state augmentation and 2- measurement differencing strategies. The proposed formulations for the EKF algorithm in this paper enable it to perform better than standard EKF in removing non-stationary contaminants. The proposed filters also preserve the clinical characteristics of ECG signals better than standard EKF. In order to show the effectiveness of the proposed EKF algorithms, their denoising performances were evaluated on the MIT-BIH Normal Sinus Rhythm Database (NSRDB) in the presence of two different types of non-stationary contaminants; 1- synthetic pink noise and 2- real muscle artifact noise extracted from Physionet noise stress database. The results showed that the proposed modified EKF frameworks significantly outperformed the standard EKF framework in non-stationary environments.

Genetic Algorithm-Based Adaptive Wiener Gain for Speech Enhancement Using an Iterative Posterior NMF

In this paper, we propose a genetic algorithm-based adaptive Wiener gain for speech enhancement using an iterative posterior non-negative matrix factorization (NMF). In the recent past, NMF-based Wiener filtering methods were used to improve the performance of speech enhancement, which has shown that they provide better performance when compared with conventional NMF methods. But performance degrades in non-stationary noise environments. Template-based approaches are more robust and perform better in non-stationary noise environments compared to statistical model-based approaches but are dependent on a priori information. Combining the approaches avoids the drawbacks of both. To improve the performance further, speech and noise bases are adapted simultaneously in the NMF approach. The usage of Super-Gaussian constraints in iterative NMF still improves the performance in non-stationary noise. The silence frame is a challenging task in the case of NMF; still there will be some amount of noise present in those frames. For further enhancement, we have combined with a genetic algorithm (GA)-based adaptive Wiener filter which performs well in denoising and also the GA search the adaptive [Formula: see text] allows us to control the trade-off between fitting the observed spectrogram of mixed speech and noise achieving high likelihood under our prior model. The proposed method outperforms other benchmark algorithms in terms of the source to distortion ratio (SDR), short-time objective intelligibility (STOI), and perceptual evaluation of speech quality (PESQ).

Novel Neuron-like Procedure of Weak Signal Detection against the Non-Stationary Noise Background with Application to Underwater Sound

The well-known method of detecting a useful signal in the presence of noise during underwater remote sensing, based on the matched filtering of the received signal with the test signal, provides the maximum signal-to-noise ratio (SNR) at the receiver output. To do this, a correlation-type criterion function (CF) is constructed for the received and test signals. In the case of large volumes of processed data, this method requires the use of large computing resources. The search for a data processing method with lower computational costs, as well as the effective application of artificial neural networks to array signal processing, motivates the authors to propose an alternative approach to the CF construction based on the McCulloch–Pitts neuron model. Such a neuron-like CF is based on a specific nonlinear transformation of the input and test signals and uses only logical operations, which require much less computational resources. The ratio of the output signal amplitude to the input noise level is indeed the maximum with matched filtering. Studies have shown that it is not this parameter that should be considered, but statistical characteristics, on the basis of which the thresholds for detecting a signal in the presence of noise are determined. Such characteristics include the probability density distributions of correlation and neuron-like CFs in the presence and absence of noise. In this case, the signal detection thresholds will be lower for the neuron-like CF than for the conventional correlation CF. The aim of this research is to increase the accuracy of the selection of a useful signal against the intense noise background when using a processor based on the neuron-like CF and to determine the conditions when the input SNR, at which signal detection is possible, is lower compared to the correlation CF. The comparative results of stochastic modeling show the effectiveness of using a new neuron-like approach to reduce the detection threshold when a chirp signal is received against a background of unsteady Gaussian noise. The advantages of the neuron-like method become significant when the statistical distribution of the additive noise does not change, but its variance increases or decreases. In order to confirm the presence of non-stationarity in real noises, experimental data obtained from the remote sounding of bottom sediments in the Black Sea are presented. The results obtained are considered to be applicable in a wide range of practical situations related to remote sensing in non-stationary environments, long-range sonar and sea bottom exploration.

Disentanglement Dynamics in Nonequilibrium Environments.

We theoretically study the non-Markovian disentanglement dynamics of a two-qubit system coupled to nonequilibrium environments with nonstationary and non-Markovian random telegraph noise statistical properties. The reduced density matrix of the two-qubit system can be expressed as the Kraus representation in terms of the tensor products of the single qubit Kraus operators. We derive the relation between the entanglement and nonlocality of the two-qubit system which are both closely associated with the decoherence function. We identify the threshold values of the decoherence function to ensure the existences of the concurrence and nonlocal quantum correlations for an arbitrary evolution time when the two-qubit system is initially prepared in the composite Bell states and the Werner states, respectively. It is shown that the environmental nonequilibrium feature can suppress the disentanglement dynamics and reduce the entanglement revivals in non-Markovian dynamics regime. In addition, the environmental nonequilibrium feature can enhance the nonlocality of the two-qubit system. Moreover, the entanglement sudden death and rebirth phenomena and the transition between quantum and classical nonlocalities closely depend on the parameters of the initial states and the environmental parameters in nonequilibrium environments.

Signal Processing of Acoustic Data for Condition Monitoring of an Aircraft Ignition System

Degradation of the ignition system can result in startup failure in an aircraft’s auxiliary power unit. In this paper, a novel acoustics-based solution that can enable condition monitoring of an APU ignition system was proposed. In order to support the implementation of this research study, the experimental data set from Cranfield University’s Boeing 737-400 aircraft was utilized. The overall execution of the approach comprised background noise suppression, estimation of the spark repetition frequency and its fluctuation, spark event segmentation, and feature extraction, in order to monitor the state of the ignition system. The methodology successfully demonstrated the usefulness of the approach in terms of detecting inconsistencies in the behavior of the ignition exciter, as well as detecting trends in the degradation of spark acoustic characteristics. The identified features proved to be robust against non-stationary background noise, and were also found to be independent of the acoustic path between the igniter and microphone locations, qualifying an acoustics-based approach to be practically viable.

Tau isoform-specific enhancement of L-type calcium current and augmentation of afterhyperpolarization in rat hippocampal neurons

Accumulation of tau is observed in dementia, with human tau displaying 6 isoforms grouped by whether they display either 3 or 4 C-terminal repeat domains (3R or 4R) and exhibit no (0N), one (1N) or two (2N) N terminal repeats. Overexpression of 4R0N-tau in rat hippocampal slices enhanced the L-type calcium (Ca2+) current-dependent components of the medium and slow afterhyperpolarizations (AHPs). Overexpression of both 4R0N-tau and 4R2N-tau augmented CaV1.2-mediated L-type currents when expressed in tsA-201 cells, an effect not observed with the third 4R isoform, 4R1N-tau. Current enhancement was only observed when the pore-forming subunit was co-expressed with CaVβ3 and not CaVβ2a subunits. Non-stationary noise analysis indicated that enhanced Ca2+ channel current arose from a larger number of functional channels. 4R0N-tau and CaVβ3 were found to be physically associated by co-immunoprecipitation. In contrast, the 4R1N-tau isoform that did not augment expressed macroscopic L-type Ca2+ current exhibited greatly reduced binding to CaVβ3. These data suggest that physical association between tau and the CaVβ3 subunit stabilises functional L-type channels in the membrane, increasing channel number and Ca2+ influx. Enhancing the Ca2+-dependent component of AHPs would produce cognitive impairment that underlie those seen in the early phases of tauopathies.

An automated pipeline for scattered light noise characterization

Scattered light noise (or scattering) affects the sensitivity of gravitational wave detectors in their detection frequency band. The mitigation of such nonlinear and nonstationary noise can be carried out experimentally and employing data analysis techniques, e.g., applying adaptive algorithms to the data affected by noise. We present gwas , a fully automated pipeline based on the time-varying filter empirical mode decomposition (tvf-EMD) algorithm, to identify, characterize, and monitor objects inducing scattering to the gravitational wave detector’s output. The tvf-EMD algorithm is suitable for decomposing signals with time-dependent frequency, such as scattering. The pipeline application to LIGO Livingston data shows that most of the scattering noise present in the third observation run was due to the penultimate mass at the end of the X-arm of the detector (EXPUM), whose motion is excited in the 0.1 Hz to 0.3 Hz frequency range (so-called microseismic band). Furthermore, we show that the pipeline can perform daily analyses, and we test it on six days of LIGO Livingston data. These analyses allowed monitoring of the onset and time evolution of scattering due to the EXPUM in connection with the variability of microseismic band noise measured at the detector site.

How Well Do Multisatellite Products Capture the Space–Time Dynamics of Precipitation? Part II: Building an Error Model through Spectral System Identification

Abstract Satellite precipitation products, as all quantitative estimates, come with some inherent degree of uncertainty. To associate a quantitative value of the uncertainty to each individual estimate, error modeling is necessary. Most of the error models proposed so far compute the uncertainty as a function of precipitation intensity only, and only at one specific spatiotemporal scale. We propose a spectral error model that accounts for the neighboring space–time dynamics of precipitation into the uncertainty quantification. Systematic distortions of the precipitation signal and random errors are characterized distinctively in every frequency–wavenumber band in the Fourier domain, to accurately characterize error across scales. The systematic distortions are represented as a deterministic space–time linear filtering term. The random errors are represented as a nonstationary additive noise. The spectral error model is applied to the IMERG multisatellite precipitation product, and its parameters are estimated empirically through a system identification approach using the GV-MRMS gauge–radar measurements as reference (“truth”) over the eastern United States. The filtering term is found to be essentially low-pass (attenuating the fine-scale variability). While traditional error models attribute most of the error variance to random errors, it is found here that the systematic filtering term explains 48% of the error variance at the native resolution of IMERG. This fact confirms that, at high resolution, filtering effects in satellite precipitation products cannot be ignored, and that the error cannot be represented as a purely random additive or multiplicative term. An important consequence is that precipitation estimates derived from different sources shall not be expected to automatically have statistically independent errors. Significance Statement Satellite precipitation products are nowadays widely used for climate and environmental research, water management, risk analysis, and decision support at the local, regional, and global scales. For all these applications, knowledge about the accuracy of the products is critical for their usability. However, products are not systematically provided with a quantitative measure of the uncertainty associated with each individual estimate. Various parametric error models have been proposed for uncertainty quantification, mostly assuming that the uncertainty is only a function of the precipitation intensity at the pixel and time of interest. By projecting satellite precipitation fields and their retrieval errors into the Fourier frequency–wavenumber domain, we show that we can explicitly take into account the neighboring space–time multiscale dynamics of precipitation and compute a scale-dependent uncertainty.

Perception of non-stationary wind noise in vehicles

Predictors of people's responses to noise inside cars are used by car companies to identify and address potential noise problems. Because significant advances have been made in the reduction of engine, powertrain, and tire/road noise, it is now important to pursue reductions in wind or aerodynamic noise. While models of loudness are commonly used to predict people's responses to stationary wind noise, some wind noises are less acceptable than is predicted by the loudness metric. Additional sound characteristics may account for this. Two listening studies were designed to examine the usefulness of including sound quality metrics in addition to loudness and sharpness in models used to predict acceptability for non-stationary wind-noise sounds, particularly noise with the kind of variations that are expected from wind gusts. Test sounds were based on recordings made in cars in a wind tunnel. A simulation method was implemented to generate sounds with controlled gusting features by modifying stationary noise recordings. A gusting metric was designed to predict subjects' acceptability responses based on the strength, modulation rate, and duration of the gusts.

Combined EEMD with a Novel Flexible Wavelet Threshold Function for Weighing Signal Denoising Approach

This paper proposes a method of combining ensemble empirical mode decomposition (EEMD) with a novel flexible wavelet threshold function to reduce the random error in the weighing result that caused by the nonstationary and nonlinear noise in quality characteristic parameter measurement equipment. The original signal is first processed by EEMD, and then, all intrinsic mode functions (IMFs) are processed by a novel flexible threshold function proposed by this paper. Finally, the denoised signal is obtained by adding reconstructed IMFs and residual. Through theoretical analysis, the proposed threshold function can retain more useful information and have continuity at the segmentation point. Moreover, the addition of adjustable parameters makes it more adaptable. Its advantages are verified by comparing the denoised results with other threshold functions in the simulation model. In weighing experiment, the validity of the novel flexible threshold function in weighing signal denoising is verified, and the effectiveness of the proposed method is also quantitatively confirmed by comparing the random errors of the original signal and the denoised signal.

Non-stationary random noise removal in ground-penetrating radar images by using self-guided filtering

Numerous high-computational-complexity algorithms have been proposed for random noise removal in ground-penetrating radar (GPR) images, which are not suitable for real-time applications. Further, most of them ignore the non-stationarity of random noise in GPR images, resulting in a limited scope for their applications. To address this issue, a self-guided filter is proposed in this study for removing non-stationary random noise in GPR images. The proposed method consists of two steps: prefiltering and final filtering. In prefiltering, the original noisy GPR image is used as the guidance and input image for guided filtering, which employs the proposed time-varying regularization parameter for obtaining the prefiltering result. In final filtering, the prefiltering result and the original noisy GPR image are used as the guidance and input image, respectively, for the proposed guided filtering combined with edge information. The edge information is obtained by using the Sobel edge detection operator to extract the prefiltering result. The experimental results demonstrate that the proposed method effectively removes the non-stationary random noise in GPR images, and it is suitable for real-time applications.