Variance Of White Noise Research Articles

Investigation on the sampling distributions of non-Gaussian wind pressure skewness and kurtosis

Accurate estimation of skewness and kurtosis is crucial for addressing issues related to non-Gaussian wind pressure distribution fitting, signal simulation, and extreme estimation. The skewness and kurtosis determined from finite-length signals are inherent random variables characterized by obvious value fluctuations. Very limited research has been conducted on the sampling distributions of skewness and kurtosis for non-Gaussian wind pressure, motivating the present study. Firstly, the investigation focuses on the non-Gaussian white noise. The expressions of main statistical indicators such as the variance, covariance, correlation coefficient, skewness, and kurtosis of the two sampling distributions are derived and then verified using the Hermite polynomial model. The primary factors influencing the sampling distribution variance (SDV) of white noise are analyzed, including the signal length and marginal moments of the parent distribution. Secondly, the concentration shifts to colored non-Gaussian processes. The composition of SDV is analyzed through theoretical derivation. On this basis, a method for estimating SDV values using the Gaussian process regression model is proposed, with accuracy and feasibility verified based on the long-duration wind pressure data measured in wind tunnel. Furthermore, the relationship between the SDVs of wind pressure processes, signal length, higher-order correlation functions, and marginal moments of the parent process is discussed.

Reconstruction of Communication Signal in Wireless Networks Based on Perturbation Compression Perception

<p>With the maturity and development of new generation communication technology, the demand for wireless network communication quality is getting higher and higher. However, the existing wireless network data transmission models are greatly affected by the signal quality in the data transmission process, which seriously affects the quality of data transmission. To address the problem of signal perturbation affecting communication quality in wireless network communication, this study designs an improved perturbation compression reconstruction algorithm that can be used to process block-structured data based on the block sparse structure in the original signal, and constructs a single-user wireless network communication data transmission model based on this algorithm. The performance simulation test of the model shows that the MSE values of the model are lower than those of the conventional and perfect schemes used as comparisons under the same noise conditions and the transmitted compressed data length conditions. When the variance of Gaussian white noise is 0.125, the MSEs of the research design model, the conventional scheme and the perfect scheme are 0.031, 0.048, and 0.047, respectively. Experimental data show that the improved disturbance compressed sensing reconstruction algorithm can better reconstruct the compressed information and reduce the information loss caused by the disturbance in the compression process on the premise of removing the signal disturbance. This research result has reference significance for improving the signal quality of wireless network communication.</p> <p> </p>

A diffusion bias-compensated LMS algorithm for distributed estimation with ARMAX models

In this paper, we study the distributed estimation problem with colored noise over adaptive networks. The nodes estimate and track an identical parameter vector in the network. The colored noise is described by a finite impulse response (FIR) model with an unknown variance, and thus leads to a bias in the diffusion least squares algorithm. Accordingly, we propose a diffusion bias-compensated LMS algorithm to deal with this situation. The performance of the proposed algorithm is analyzed, which shows that it can achieve the mean-square stability on the condition that the step size is sufficiently small. Furthermore, we obtain the corresponding closed mean-square deviation containing the white noise variance. Finally, the given simulations show the effectiveness of our proposed algorithm.

Construction of Biologic Microscopic Image Segmentation Model Based on Smoothing of Fourth-Order Partial Differential Equation.

In order to solve the problem of microscopic image noise, a biological microscopic image segmentation model based on the smoothing of the fourth-order partial differential equation was proposed. Based on the functional description of image smoothness by directional curvature mode value, a fourth-order PDE image denoising model is derived, which can effectively reduce noise while preserving edges. The result of this method is piecewise linear image, and the gradient at the edge of the target has a step. Using the feature of noise reduction, a new geodesic active contour model is proposed. The experiment result shows that when the variance of Gaussian white noise is 15, the enhancement and denoising effects of the proposed method are 80.35% and 69.84 higher than those of the original vibration filtering method and L. Alvarez method. In terms of time, the proposed method is 1.3075 seconds slower than the original vibration filtering method and 17.5754 seconds faster than the L. Alvarez method. When the variance of Gaussian white noise is 25, the enhancement and denoising effects of the proposed method are 97.79% and 81.16 higher than those of the original vibration filtering method and L. Alvarez method. In terms of time, the proposed method is 1.3246 seconds slower than the original vibration filtering method and 17.5796 seconds faster than the L. Alvarez method. Conclusion. The new model is not only stable but also has strong ability of contour extraction and fast convergence.

Blind estimation of noise level based on pixels values prediction

Noise parameters estimation is needed for many tasks of digital image processing. Many efficient algorithms of noise variance estimation were proposed during last two decades. However, most of those estimators are efficient only for a specific kind of noise for which they were designed. For example, methods of estimation of variance of white additive Gaussian noise (AWGN) fail in the case of additive colored Gaussian noise (ACGN) or for noises with other distributions. In this paper a new fully blind method of noise level estimation is proposed. For a given image, a distorted image with a removed part of pixels (around 10%) is generated. Then an inpainting (or impulse noise removal) method is used to recover missed pixels values. The difference between true and recovered values is used for a robust estimation of noise level. The algorithm is applied for different image scales to estimate noise spectrum. In the paper we propose a convolutional neural network PIXPNet for effective prediction of values of missing pixels. A comparative analysis shows that the proposed PIXPNet provides smallest error of recovered pixels values among all existing methods. A good efficiency of usage of the proposed approach in both AWGN and spatially correlated noise suppression is demonstrated.

Autoregressive model of an underwater acoustic channel in the frequency domain

The underwater acoustic (UWA) channel model based on the multipath delay–amplitude or the angle of departure (AoD)–angle of arrival (AoA) require many parameters to describe a broadband underwater acoustic (UWA) channel. In this paper, an autoregressive (AR) model is developed to describe the channel in the frequency domain with few parameters. The AR model used here is with an order P, where P is also related to the number of main multipath clusters. Hence, only P + 1 parameters, which consist of the variance of the complex Gaussian white noise (CGWN) and the P pole values of the AR model, are required to describe UWA channel. Each pole value is corresponded to a multipath cluster in the channel, where its phase is correlated with the average multipath delay, and its absolute value is related to the multipath energy. A comprehensive analysis was performed to characterize the statistical distribution of each pole value and the CGWN variance. The results showed that the absolute value and phase of each pole satisfied the Weibull and gamma distributions, respectively, and the variance obeyed a lognormal distribution. Simulation channels were generated with different distributions of the AR model parameters, and the root mean square (RMS) delay obeyed a similar cumulative distribution function as the measured channel.

Application of Box-Jenkins Models to the Tourist Inflow in Bhutan

Bhutan has now increasingly become a popular destination for many international tourists. Tourism in Bhutan is considered as one of the largest foreign earning industries. The number of tourist inflow in the country is increasing year by year. Forecasting is very necessary for administration and tourist agent for creating awareness and planning for the future development. It can also predict the future trends as accurately as possible and helps in staying one step ahead of the competition. This study aims to apply mathematical model for forecasting monthly tourist inflow from Malaysia, Singapore, China, USA, England, France, Germany, Thailand, Australia and Japan to Bhutan. The Box-Jenkins model is used to identify the parameters of Autoregressive integrated moving average (ARIMA) model of monthly tourist visited data of above mentioned countries in the period 2011-2015 obtained from Tourism Council of Bhutan. An Akaike's Information Criterion, Schwartz's Bayesian Criterion and estimate variance of white noise are used throughout to test for the identification of best fit model. Further, the periodogram analysis was used to confirm the seasonal period of the model. The results showed ARIMA model for Thai, Chinese, Malaysian and Japanese, while seasonal ARIMA for American, Australian, British, French, Singaporean and German. Further, seasonal ARIMA model was obtained as the best fit model for the overall data. These models are illustrated and could possibly forecast the monthly tourist inflow of one year ahead with acceptable accuracy.

A STATISTICAL OVERVIEW ON SLEEP SCORING

In this study, sleep electroencephalography (EEG) which is frequently used in statistical modelling has been modelled with the autoregressive (AR) time-series model and what kind of a structure the variance of the term white noise included in the model represented in different sleep stages has been observed. Taking all of the stages scored in accordance with Rechtschaffen and Kales criterion into account separately, epoches in each stage have been modelled with the AR and the variance of the term white noise in this model has been monitored. The study has evaluated the sleep EEG variances of a subject. In accordance with the results, the heterogeneity at Stage 2 was thought to be the reason why the objective differences appeared in scoring. It is thought that this data pointed out a necessity that the period in Rechtschaffen and Kales scoring which is called Stage 2 must be revised.

Cell-filtering-based multi-scale Shannon–Cosine wavelet denoising method for locust slice images

The locust slice images have all the features such as strong self-similarity, piecewise smoothness and nonlinear texture structure. Multi-scale interpolation operator is an effective tool to describe such structures, but it cannot overcome the influence of noise on images. Therefore, this research designed the Shannon–Cosine wavelet which possesses all the excellent properties such as interpolation, smoothness, compact support and normalization, then constructing multi-scale wavelet interpolative operator, the operator can be applied to decompose and reconstruct the images adaptively. Combining the operator with the local filter operator (mean and median), a multi-scale Shannon–Cosine wavelet denoising algorithm based on cell filtering is constructed in this research. The algorithm overcomes the disadvantages of multi-scale interpolation wavelet, which is only suitable for describing smooth signals, and realizes multi-scale noise reduction of locust slice images. The experimental results show that the proposed method can keep all kinds of texture structures in the slice image of locust. In the experiments, the locust slice images with mixture noise of Gaussian and salt–pepper are taken as examples to compare the performances of the proposed method and other typical denoising methods. The experimental results show that the Peak Signal-To-Noise Ratio (PSNR) of the denoised images obtained by the proposed method is greater 27.3%, 24.6%, 2.94%, 22.9% than Weiner filter, wavelet transform method, median and average filtering, respectively; and the Structural Similarity Index (SSIM) for measuring image quality is greater 31.1%, 31.3%, 15.5%, 10.2% than other four methods, respectively. As the variance of Gaussian white noise increases from 0.02 to 0.1, the values of PSNR and SSIM obtained by the proposed method only decrease by 11.94% and 13.33%, respectively, which are much less than other 4 methods. This shows that the proposed method possesses stronger adaptability.

A novel local variance-based filtering method for denoising remote sensing images

ABSTRACTIn this paper, a novel filtering method is designed for denoising remote sensing image. Firstly, the image domain of noisy image is partitioned into blocks for estimating the variance of Gaussian white noise. Secondly, based on the fact that the variance of the textural region is always larger than that of the homogeneous region, the noisy image is roughly divided into homogeneous and textural regions. Thirdly, a novel filter is designed and is used to reduce the noises. To this end, adaptive windows with appropriate shape and size are selected for each pixel. With the pixels in the window(s), the noise intensity of the central pixel is estimated and further qualified as a noise level. Based on noise levels, pixel values within the filter window are first updated and then filtered by using the proposed filter. Compared with other filtering methods, better performance is achieved in both noise smoothing and detail conserving.

A design for a dynamic biomimetic sonarhead inspired by horseshoe bats

The noseleaf and pinnae of horseshoe bats (Rhinolophus ferrumequinum) have both been shown to actively deform during biosonar operation. Since these baffle structures directly affect the properties of the animals biosonar system, this work mimics horseshoe bat sonar system with the goal of developing a platform to study the dynamic sensing principles horseshoe bats employ. Consequently, two robotic devices were developed to mimic the dynamic emission and reception characteristics of horseshoe bats. The noseleaf and pinnae shapes were modeled as smooth blanks matched to digital representations of a horseshoe bat specimens noseleaf and pinnae. Local shape features mimicking structures on the pinnae and noseleaf were added digitally. Flexible baffles with local shape feature combinations were manufactured and paired with actuation mechanisms to mimic pinnae and noseleaf deformations in vivo. Two noseleaves with and without local shape features were considered. Each noseleaf baffle was mounted to a platform called the dynamic emission head to actuate three surface elements of the baffle. Similarly, 12 pinna realizations composed of combinations of three local shape features were mounted to a platform called the dynamic reception head to deform the left and right pinnae independently. Motion of the noseleaf and pinnae were synchronized to the incoming and outgoing sonar waveform, and the joint time-frequency properties of the noseleaf and pinnae local feature combinations and pairs of pinnae and noseleaf thereof were characterized across spatial direction. Amplitude modulations to the outgoing and incoming sonar pulse information across spatial direction were observed for all pinnae and noseleaf local shape feature combinations. Peak modulation variance generated by motion of the pinnae and combinations of the noseleaf and pinnae approached a white Gaussian noise variance bound. It was found the dynamic emitter generated less modulation than either the combined or reception scenarios.

Blind estimation of white Gaussian noise variance in highly textured images

In the paper, a new method of blind estimation of noise variance in a single highly textured image is proposed. An input image is divided into 8x8 blocks and discrete cosine transform (DCT) is performed for each block. A part of 64 DCT coefficients with lowest energy calculated through all blocks is selected for further analysis. For the DCT coefficients, a robust estimate of noise variance is calculated. Corresponding to the obtained estimate, a part of blocks having very large values of local variance calculated only for the selected DCT coefficients are excluded from the further analysis. These two steps (estimation of noise variance and exclusion of blocks) are iteratively repeated three times. For the verification of the proposed method, a new noise-free test image database TAMPERE17 consisting of many highly textured images is designed. It is shown for this database and different values of noise variance from the set {25, 49, 100, 225}, that the proposed method provides approximately two times lower estimation root mean square error than other methods.

Measurement variance ignorant target motion analysis

The paper is devoted to Bayesian target motion analysis (TMA) for the case when the variance of additive white zero-mean Gaussian measurement noise is unknown. Two Rao–Blackwellised particle filters for TMA are developed, which jointly estimate the target state and the measurement variance. The error performance of the two particle filters is compared against the theoretical Cramer–Rao lower bound. The bound suggests the error in target state estimation is not affected by the ignorance of the measurement noise variance. Both developed TMA algorithms reach this theoretical bound, however, one is significantly faster.

RLS Wiener estimators from observations with multiple and random delays in linear discrete-time stochastic systems

This paper designs a new recursive least-squares (RLS) Wiener fixed-point smoother and filter from randomly delayed observed values by multiple sampling times in linear discrete-time stochastic systems. The actual observed value is generated in terms of the observed values y¯(k-(j-1)) with the probability pj(k),1⩽j⩽N. It is assumed that the delay measurements are characterized by Bernoulli random variables. y¯(k) is given as a sum of the signal and the white observation noise. The RLS Wiener estimators use the following information: (a) the system matrix; (b) the observation matrix; (c) the variance of the state vector; (d) the delay probabilities pj(k) and (e) the variance of white observation noise.

Specific conductivity sensor performance: II. Field evaluation

The US Environmental Protection Agency (USEPA) has issued guidance on the specific conductivity (EC25°C) of waters discharged from mined lands in the Appalachian Coal Belt Region of the USA. In this guidance, the USEPA states that these waters should have an EC25°C less than 300–500 μS cm−1. Such a requirement places great importance on accurately determining EC25°C. Building upon a laboratory-based evaluation of four types of commercially available continuous logging conductivity sensors, this study examined sensor performance in the more harsh and variable field environments at forested and mined land streams in eastern Kentucky. The objectives of this study were to calculate the white noise variance associated with each sensor type and to evaluate white noise variance in relation to variations in EC25°C and discharge. Results of the study indicate that predominant increases in EC25°C, and to some extent increases in discharge, explain between 35 and 65% of the white noise variance.

Wavelet Transform Denoise of PCB Drilling Force Signal

In the PCB micro drilling, because the force signal is tiny, and when the micro-drill drill to a certain degree of multilayer PCB, alternate force signals will not appear obvious, through to the drilling force signal analysis, we can know the drill bit position and the materials to the influence of the drill failure, so the drilling force signals denoise seems extremely important. In the processing of the non-stationary signal, traditional signal processing method has a certain extent of insufficient, using the wavelet packet decomposition signal, the white noise variance and amplitude decrease with the increase of wavelet scales, but the signal variance and amplitude has nothing to do with the wavelet transform. According to the view of the signal energy, first of all, we make the multiscale decomposition of the signal, then, by using some of the wavelet packet that has efficient energy to reconstruct the original signal. Comparing with the traditional threshold denoising ,using this method in the test signal to deal with the noise can effectively eliminate the white noise interference, and has good denoising effects besides the simple calculation.

Homogeneity Localization Using Particle Filters With Application to Noise Estimation

This paper proposes a method for localizing homogeneity and estimating additive white Gaussian noise (AWGN) variance in images. The proposed method uses spatially and sparsely scattered initial seeds and utilizes particle filtering techniques to guide their spatial movement towards homogeneous locations. This way, the proposed method avoids the need to perform the full search associated with block-based noise estimation methods. To achieve this, the paper proposes for the particle filter a dynamic model and a homogeneity observation model based on Laplacian structure detectors. The variance of AWGN is robustly estimated from the variances of blocks in the detected homogeneous areas. A proposed adaptive trimmed-mean based robust estimator is used to account for the reduction in estimation samples from the full search approach. Our results show that the proposed method reduces the number of homogeneity measurements required by block-based methods while achieving more accuracy.

Design of RLS Wiener estimators from randomly delayed observations in linear discrete-time stochastic systems

This paper presents the design of a new recursive least-squares (RLS) Wiener filter and fixed-point smoother based on randomly delayed observed values by one sampling time in linear discrete-time wide-sense stationary stochastic systems. The mixed observed value y( k) consists of the past observed value y ¯ ( k - 1 ) by one sampling time with the probability p( k) and of the current observed value y ¯ ( k ) at time k with the probability 1 − p( k). It is assumed that the delayed measurements are characterized by Bernoulli random variables. The observation y ¯ ( k ) is given as the sum of the signal z( k) and the white observation noise v( k). The RLS Wiener estimators explicitly require the following information: (a) the system matrix for the state vector; (b) the observation matrix; (c) the variance of the state vector; (d) the delayed probability p( k); (e) the variance of white observation noise v( k).

Noise Parameter Estimation From Quantized Data

In this paper, the parametric estimation of the variance of white Gaussian noise is considered when available data are obtained from a quantized noisy stimulus. The Crameacuter-Rao lower bound is derived, and the statistical efficiency of a maximum-likelihood parametric estimator is discussed, along with the estimation algorithm proposed in IEEE Standard 1241

On Estimation of Autoregressive Signals in the Presence of Noise

Estimation of autoregressive (AR) signals measured in white noise is considered. A well-known fact is that the measurement noise causes the least-squares (LS) estimate of the AR parameters to be biased. The kernel of an alternative method to be proposed is that, unlike the previous LS-based methods, a noniterative estimation scheme is established for the measurement white noise variance - the source of the bias. Numerical results demonstrate that the proposed method is much more cost effective in terms of computations and accuracy than the previous LS-based methods. The establishment of this noniterative unbiased estimation method also provides a mechanism for better understanding of the family of the LS-based methods