Stationary Gaussian Noise Research Articles

A Joint Denoising Technique for Mixed Gaussian–Impulse Noise Removal in HSI

Hyperspectral imaging (HSI) is the procedure of acquiring a scene over a wide range of electromagnetic spectrum for the purpose of detailed analysis and prediction. The occurrence of noise during the acquisition procedure, however, poses a limitation on this imaging system. Noise in HSI is classified as a mixture of Gaussian and impulse noise statistics, and noise removal or denoising forms an integral part of this imaging system. In this paper, we consider the problem of removing this mixed Gaussian-impulse noise from HSI data-sets by formulating a joint optimization problem based on the maximum <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posteriori</i> (MAP) estimates for Gaussian and impulse noise distributions. The proposed method is then solved using an efficient minimization strategy realizied through half-quadratic split. Extensive experimentation on synthetic and real HSI data-sets corroborate the effectiveness of the proposed denoising technique.

Advances in UAV-Assisted Localization: Joint Source and UAV Parameter Estimation

This paper presents efficient estimators to address the problem of source localization aided by unmanned aerial vehicles (UAVs) with unknown location parameters. Leveraging semidefinite relaxation technique and successive weighted least squares estimation, the source and UAV parameters are simultaneously estimated in both mixed line-of-sight/non-line-of-sight (NLOS) and NLOS scenarios. The proposed estimators are shown to approximately achieve the Cramer-Rao bound (CRB) under mild Gaussian noise conditions when the measurement noises are small compared to the associated ranges. Numerical simulations demonstrate that localization without prior UAV location information is still possible with a meter-level positioning and sub-meter per seconds velocity estimation accuracy.

Performance Analysis of the Standard Constrained Maximum Versoria Criterion Based Adaptive Algorithm

Recently, robust adaptive filtering approaches relied on the Maximum Versoria Criterion (MVC) have gained the attention of researchers and have been widely studied. In this brief, with the energy conservation approach, transient and steady-state mean-square deviation (MSD) analysis of the standard constrained MVC (CMVC) are derived under both Gaussian and non-Gaussian noise distributions. For a Gaussian noise condition, an accurate solution is obtained, while for non-Gaussian noise conditions, we used approximate Taylor's expansion to derive the transient and steady-state MSD. Finally, we evaluated the theoretical analysis with some numerical simulations of system identification in different Gaussian and non-Gaussian noise scenarios to validate the finding.

Estimation of a Function in a Gaussian Stationary Noise

Estimation of a Function in a Gaussian Stationary Noise

Controlled Parameter Estimation for The AR(1) Model with Stationary Gaussian Noise

This paper deals with the maximum likelihood estimator for the parameter of first-order autoregressive models driven by the stationary Gaussian noises (Colored noise) together with an input. First, we will find the optimal input that maximizes the Fisher information, and then, with the method of the Laplace transform, both the asymptotic properties and the asymptotic design problem of the maximum likelihood estimator will be investigated. The results of the numerical simulation confirm the theoretical analysis and show that the proposed maximum likelihood estimator performs well in finite samples.

White-noise fluctuation theorem for Langevin dynamics

Fluctuation theorems (FTs) based on time-reversal have provided remarkable insight into the non-equilibrium statistics of thermodynamic quantities like heat, work, and entropy production. These types of laws impose constraints on the distributions of certain trajectory functionals that reflect underlying dynamical symmetries. In this work, we introduce a detailed FT for Langevin dynamics that follows from the statistics of Gaussian white noise rather than from time-reversal. The theorem, which originates from a point-wise symmetry in phase space, holds individually for each degree of freedom coupled to additive or multiplicative noise. The relation is independent of the phase space distribution generated by the dynamics and can be used to derive a versatile parameter inference algorithm applicable to the a wide range of systems, including non-conservative and non-Markovian ones.

Robust Initial Alignment Based on Unscented Information Kalman Filter

The velocity of the odometer (OD) and Doppler velocity log (DVL) is easily contaminated by non-Gaussian noise, and the prior information of the state vector is usually hard to estimate accuracy enough, which will lead to the performance of alignment to decline or even divergent. Considering the error characteristic model has very significant nonlinear characteristics, a robust unscented information Kalman filter (RUIKF) algorithm for dynamic initial alignment is proposed in this article to suppress the influence of interference noise. The RUIKF algorithm first calculates the Mahalanobis distance (MD) between observation and the innovation of observation, and an amplification factor is designed to modify the estimation of the measurement noise covariance matrix and then take the modified measurement noise covariance matrix to update the measurement. The state error is estimated by the RUIKF to modify the strapdown inertial navigation system (SINS) navigation solution. Initial alignment experiments are carried out by the RUIKF and unscented information Kalman filter (UIKF) algorithm, respectively, under the conditions of outliers and mixed Gaussian distribution noise. The results show that the RUIKF can suppress the effect of outliers and non-Gaussian noise when the velocity of the OD (or DVL) is contaminated. The experiment results also verify the feasibility and effectiveness of the RUIKF algorithm on the SINS/DVL/OD integrated dynamic initial alignment.

Single-channel speech enhancement using implicit Wiener filter for high-quality speech communication

Speech enables easy human-to-human communication as well as human-to-machine interaction. However, the quality of speech degrades due to background noise in the environment, such as drone noise embedded in speech during search and rescue operations. Similarly, helicopter noise, airplane noise, and station noise reduce the quality of speech. Speech enhancement algorithms reduce background noise, resulting in a crystal clear and noise-free conversation. For many applications, it is also necessary to process these noisy speech signals at the edge node level. Thus, we propose implicit Wiener filter-based algorithm for speech enhancement using edge computing system. In the proposed algorithm, a first order recursive equation is used to estimate the noise. The performance of the proposed algorithm is evaluated for two speech utterances, one uttered by a male speaker and the other by a female speaker. Both utterances are degraded by different types of non-stationary noises such as exhibition, station, drone, helicopter, airplane, and white Gaussian stationary noise with different signal-to-noise ratios. Further, we compare the performance of the proposed speech enhancement algorithm with the conventional spectral subtraction algorithm. Performance evaluations using objective speech quality measures demonstrate that the proposed speech enhancement algorithm outperforms the spectral subtraction algorithm in estimating the clean speech from the noisy speech. Finally, we implement the proposed speech enhancement algorithm, in addition to the spectral subtraction algorithm, on the Raspberry Pi 4 Model B, which is a low power edge computing device.

Embedding Soft Thresholding Function into Deep Learning Models for Noisy Radar Emitter Signal Recognition

Radar emitter signal recognition under noisy background is one of the focus areas in research on radar signal processing. In this study, the soft thresholding function is embedded into deep learning network models as a novel nonlinear activation function, achieving advanced radar emitter signal recognition results. Specifically, an embedded sub-network is used to learn the threshold of soft thresholding function according to the input feature, which results in each input feature having its own independent nonlinear activation function. Compared with conventional activation functions, the soft thresholding function is characterized by flexible nonlinear conversion and the ability to obtain more discriminative features. By this way, the noise features can be flexibly filtered while retaining signal features, thus improving recognition accuracy. Under the condition of Gaussian and Laplacian noise with signal-to-noise ratio of −8 dB to −2 dB, experimental results show that the overall average accuracy of soft thresholding function reached 88.55%, which was 11.82%, 8.12%, 2.16%, and 1.46% higher than those of Sigmoid, PReLU, ReLU, ELU, and SELU, respectively.

Absence of stationary states and non-Boltzmann distributions of fractional Brownian motion in shallow external potentials

We study the diffusive motion of a particle in a subharmonic potential of the form U(x) = |x| c (0 < c < 2) driven by long-range correlated, stationary fractional Gaussian noise ξ α (t) with 0 < α ⩽ 2. In the absence of the potential the particle exhibits free fractional Brownian motion with anomalous diffusion exponent α. While for an harmonic external potential the dynamics converges to a Gaussian stationary state, from extensive numerical analysis we here demonstrate that stationary states for shallower than harmonic potentials exist only as long as the relation c > 2(1 − 1/α) holds. We analyse the motion in terms of the mean squared displacement and (when it exists) the stationary probability density function. Moreover we discuss analogies of non-stationarity of Lévy flights in shallow external potentials.

Water Cycle Algorithm Based Parametric Tuning of Non-Negative LMMN Control of Grid Tied Renewable Energy Systems

ABSTRACT This work proposes a hydrological cycle-based optimisation technique for performance enhancement of a non-negative least mean mixed norm (NNLMMN) based voltage source control (VSC) for a three-phase grid integrated wind/photovoltaic (PV) system. Water cycle algorithm (WCA) is employed to tune the proportional–integral (PI) controller parameters of VSC to regulate voltage variations at DC link generated during dynamic load and wind conditions. This results in generation of a specific loss component (Iloss) of current to boost the performance of VSC. The NNLMMN control deals with system identification troubles with a non-negativity limitation in varied Gaussian noise conditions. It generates accurate Iloss to upgrade the ability of VSC to accurately extricate weight signals and the fundamental load current component in terms of improvement in DC link voltage (vdc) and total harmonic distortion. The proposed algorithm mitigates problems like voltage fluctuations besides performing operations like reactive power compensation, enhancement of power quality, load and power balancing at the point of coupling during steady-state and dynamic conditions. In conjunction with the NNLMMN algorithm, the proposed technique reduces the surplus mean square error iteratively, resulting in a compact expression of step size. The proposed topology stands out with an improved performance of vdc under wind gusts and the well-known bell-shaped irradiance curve. For relative evaluations, the performance of non-optimised PI and particle swarm optimised PI has been added to analyse the improved response of vdc and Iloss. Extensive simulation results obtained in MATLAB/Simulink are exhibited to corroborate the efficacy of the suggested system.

Moment estimator for an AR(1) model driven by a long memory Gaussian noise

In this paper, we consider an inference problem for the first order autoregressive process driven by a given long memory stationary Gaussian noise. Suppose that the covariance function of the noise is positive and can be expressed as |k|2H−2 times a positive function slowly varying at infinity. The fractional Gaussian noise and the fractional ARIMA(0, d, 0) model with d∈(0,12) and some others Gaussian noise are special examples that satisfy this assumption. We propose a moment estimator and prove the strong consistency, the asymptotic normality and the almost sure central limit theorem. Moreover, we give the upper Berry–Esséen bound by means of Fourth moment theorem.

Reliable UAV Monitoring System Using Deep Learning Approaches

In recent years, unmanned aerial vehicles (UAV) or drones have become ubiquitous in our daily lives, bringing great convenience to our lives and playing a pivotal role in future wireless networks and the Internet of things. One of the major problems associated with the UAV is the heterogeneous nature of such deployments; this heterogeneity poses many challenges, particularly in the areas of security and privacy. The key to solving these problems is to accurately identify and authenticate drones. In this article, a reliable UAV identify framework based on radio frequency fingerprint is proposed. First, we established a wireless signal label architecture and systematically collected, analyzed, and recorded the radio frequency signals of different UAVs in different flight modes and different distances in the telemetry link, and established UAV signal datasets. Then, the intelligent algorithm and anti-UAV system are designed by using the collected dataset, and the feasibility of the developed dataset for detecting and identifying UAVs is verified by using machine learning and deep learning. The simulation results show that under the condition of Gaussian white noise, the method based on deep learning achieves high reliability, and when the SNR is not less than 5dB, the model achieves more than 95% of the monitoring and recognition accuracy. Finally, we discussed the possible applications of the dataset in the future.

Conical Localization From Angle Measurements: An Approximate Convex Solution

For several years, a substantial effort has been devoted to the study of 3-D source localization based on 2-D arrays by measuring the well-known azimuth and elevation angles. However, studies on 3-D source localization performed by 1-D arrays are still lacking. Perhaps, the most important drawback in the deployment of a 2-D array structure lies in the fact that it needs a planar space, which might not be available in some applications. This letter concentrates on the problem of 3-D source localization based on 1-D angle measurement provided by a linear array. Different from the traditional 2-D structures where each measurement induces a straight line, each measurement in the 1-D array results in a conic surface originating at the array location. The localization problem is formulated as a constrained weighted least squares optimization problem and the semidefinite relaxation technique has been utilized to recast it as a convex optimization problem. Numerical simulation indicates that the performance of the proposed method outperforms the existing estimator and can reach the Cramer&#x2013;Rao lower bound under mild Gaussian noise conditions.

Calibration uncertainty’s impact on gravitational-wave observations

Our ability to characterize astrophysical gravitational waves depends on our understanding of the detectors used to observe them. Specifically, our ability to calibrate current kilometer-scale interferometers can potentially confound the inference of astrophysical signals. Current calibration uncertainties are dominated by systematic errors between the modeled and observed detector responses and are well described by a Gaussian process. I exploit this description to analytically examine the impact of calibration uncertainty. I derive closed-form expressions for the conditioned likelihood of the calibration error given the observed data and an astrophysical signal (astrophysical calibration) as well as for the marginal likelihood for the data given a signal (integrated over the calibration uncertainty). I show that calibration uncertainty always reduces search sensitivity and the amount of information available about astrophysical signals. Additionally, calibration uncertainty will fundamentally limit the precision to which loud signals can be constrained, a crucial factor when considering the scientific potential of proposed third-generation interferometers. For example, I estimate that with 1% uncertainty in the detector response's amplitude and phase, one will only be able to measure the leading-order tidal parameter ($\stackrel{\texttildelow{}}{\mathrm{\ensuremath{\Lambda}}}$) for a $1.4+1.4\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ system to better than $\ifmmode\pm\else\textpm\fi{}1$ ($\ensuremath{\sim}0.2%$ relative uncertainty) for signals with signal-to-noise ratios $\ensuremath{\gtrsim}{10}^{4}$. At this signal-to-noise ratio, calibration uncertainty increases ${\ensuremath{\sigma}}_{\stackrel{\texttildelow{}}{\mathrm{\ensuremath{\Lambda}}}}$ by a factor of 2 compared to stationary Gaussian noise alone. Furthermore, 1% calibration uncertainty limits the precision to always be ${\ensuremath{\sigma}}_{\stackrel{\texttildelow{}}{\mathrm{\ensuremath{\Lambda}}}}\ensuremath{\gtrsim}0.5$. At more modest signal-to-noise ratios ($\ensuremath{\lesssim}30$) characteristic of the current set of detected events, the uncertainty in $\stackrel{\texttildelow{}}{\mathrm{\ensuremath{\Lambda}}}$ will be ${\ensuremath{\sigma}}_{\stackrel{\texttildelow{}}{\mathrm{\ensuremath{\Lambda}}}}\ensuremath{\gtrsim}100$ and will be dominated by the Gaussian noise rather than calibration uncertainty. I also show how to best select the frequencies at which calibration should be precisely constrained in order to minimize the information lost about astrophysical parameters. It is not necessary to constrain the calibration errors to be small at all frequencies to perform precise astrophysical inference for individual signals.

Real-time image denoising of mixed Poisson–Gaussian noise in fluorescence microscopy images using ImageJ

Fluorescence microscopy imaging speed is fundamentally limited by the measurement signal-to-noise ratio (SNR). To improve image SNR for a given image acquisition rate, computational denoising techniques can be used to suppress noise. However, common techniques to estimate a denoised image from a single frame either are computationally expensive or rely on simple noise statistical models. These models assume Poisson or Gaussian noise statistics, which are not appropriate for many fluorescence microscopy applications that contain quantum shot noise and electronic Johnson–Nyquist noise, therefore a mixture of Poisson and Gaussian noise. In this paper, we show convolutional neural networks (CNNs) trained on mixed Poisson and Gaussian noise images to overcome the limitations of existing image denoising methods. The trained CNN is presented as an open-source ImageJ plugin that performs real-time image denoising (within tens of milliseconds) with superior performance (SNR improvement) compared to conventional fluorescence microscopy denoising methods. The method is validated on external datasets with out-of-distribution noise, contrast, structure, and imaging modalities from the training data and consistently achieves high-performance ( &gt; --> 8 d B ) denoising in less time than other fluorescence microscopy denoising methods.

Temporal separation of whale vocalizations from background oceanic noise using a power calculation

The process of analyzing audio signals in search of cetacean vocalizations is in many cases a very arduous task, requiring many complex computations, a plethora of digital processing techniques and the scrutinization of an audio signal with a fine comb to determine where the vocalizations are located. To ease this process, a computationally efficient and noise-resistant method for determining whether an audio segment contains a potential cetacean call is developed here with the help of a robust power calculation for stationary Gaussian noise signals and a recursive method for determining the mean and variance of a given sample frame. The resulting detector is tested on audio recordings containing southern right whale sounds and its performance is compared to a contemporary energy detector and a popular deep learning method. The detector exhibits good performance at moderate-to-high signal-to-noise ratio values. The detector succeeds in being easy to implement, computationally efficient to use and robust enough to accurately detect whale vocalizations in a noisy underwater environment.

Adaptive identification under the maximum correntropy criterion with variable center

The problem of identifying the parameters of a linear object in the presence of non-Gaussian noise is considered. The identification algorithm is a gradient procedure for maximizing the functional, which is a correntropy. This functionality allows you to get estimates that have robust properties. In contrast to the commonly used Gaussian kernels, the centers of which are at zero and effective for distributions with zero mean, the paper considers a modification of the criterion suitable for distributions with nonzero mean. The modification is to use correntropy with a variable center The use of Gaussian kernels with a variable center will allow us to estimate unknown parameters under Gaussian and non-Gaussian noises with zero and non-zero mean distributions and provide an opportunity to develop new technologies for data analysis and processing. It is important to develop a robust identification algorithm based on correntropy with variable center. Their properties in the identification of stationary and non-stationary objects are the subject of research. The goal is to develop a robust identification algorithm that maximizes the criterion of correntropy with a variable center using center configuration procedures and kernel width and to study its convergence in stationary and non-stationary cases under non-Gaussian noise. Expressions for steady-state value of the estimation error are obtained, which depend on the type of noise distribution and the degree of non-stationarity of the estimated parameters The following tasks are solved: to investigate the convergence of the algorithm and determine the conditions for the stability of the established identification process. Methods of estimation theory (identification) and probability theory are used. The following results were obtained: 1) the developed algorithm provides robust estimates in the presence of noises having a distribution with zero and non-zero mean; 2) its convergence was studied in stationary and non-stationary cases under conditions of Gaussian and non-Gaussian noise; 3) simulation of the algorithm was carried out. 1) the developed algorithm consists in the development of a robust identification algorithm that maximizes the criterion of correntropy with a variable center; 2) its convergence in stationary and non-stationary cases in the conditions of Gaussian and non-Gaussian noises is investigated; 3) simulation of the algorithm is performed. Conclusions: The results of the current study will improve existing data processing technologies based on robust estimates and accelerate the development of new computing programs in real time.

Precipitation Retrieval from Fengyun-3D Microwave Humidity and Temperature Sounder Data Using Machine Learning

As an important component of the Earth system, precipitation plays a vital role in regional and global water cycles. Based on Microwave Humidity and Temperature Sounder (MWHTS) onboard FY-3D satellite, four machine learning models, random forest regression (RFR), support vector machine (SVM), multilayer perceptron (MLP), and gradient boosting regression tree (GBRT), are implemented to retrieve precipitation rate, and verified with Integrated Multi-satellite Retrievals for GPM (IMERG). This paper determines the optimal hyperparameters of the machine models and proposes three linear combinations of MWHTS channels (183.31 ± 1.0–183.31 ± 3.0 GHz, 183.31 ± 1.0–183.31 ± 7.0 GHz, and 183.31 ± 3.0–183.31 ± 7.0 GHz), which can better characterize precipitation of different intensities. With the inclusion of three linear combinations, the performances of all four machine learning models are significantly improved. It is concluded that the RFR and GBRT have the best retrieval accuracy. Over ocean, the MSE, MAE, and R2 values of precipitation estimates using RFR are 1.75 mm/h, 0.44 mm/h, and 0.80, respectively, and are 1.80 mm/h, 0.45 mm/h, and 0.78 for GBRT. Simultaneously, this paper analyzes the retrieval results from the perspective of the different rain rates and temporal matching difference between MWHTS and IMERG data. The RFR and GBRT also maintain the best retrieval accuracy under the condition of Gaussian noise, indicating the relatively strong robustness and antinoise performance of ensemble learning models for precipitation retrieval.

2ASK System Modeling and Simulation

The communication network of our country is developing vigorously, and the digital communication system has a certain development prospect. However, for wireless signal transmission, signal modulation is needed to ensure the output results. To use the limited bandwidth to transmit digital signals more efficiently, the corresponding digital signals need to be modulated by the carrier. In this paper, the digital signal is transmitted by carrier modulation, and under the condition of Gaussian white noise, the modelling and simulation of 2ASK modulation and demodulation system are realized by using Simulink and m file respectively, and the anti-noise performance of the system can be seen. And through the m file to achieve non-coherent demodulation and coherent demodulation through the Simulink, we can see the advantages and disadvantages of the two ways. At the end of the paper, the bit error rate of the 2ASK signal is analyzed.