Noise Level Estimation Research Articles

Ramanujan Sums as Derivatives and Applications

In 1918, S. Ramanujan defined a family of trigonometric sums now known as Ramanujan sums. In this letter, we define a class of operators based on the Ramanujan sums termed here as Ramanujan class of operators. We then prove that these operators possess properties of first derivative and with a particular shift, of second derivative also. Applications of Ramanujan class of operators for edge detection and noise level estimation are also demonstrated.

Machine learning for spatial interpolation of noise monitor levels

Continuously recording noise monitoring stations provide feedback of the noise environment at monitor locations. While this feedback is useful, it only provides information at a few point locations and, in many cases, it is of interest to know the noise level(s) at locations between and beyond noise monitoring locations. In this study, we test several machine learning models (e.g., random forests, support vector machines, and neural networks) for their ability to predict noise levels using a small number of noise monitors. Unlike the hybrid geostatistical-acoustical method proposed by Nykaza [Nykaza, Ph.D. thesis, 2013] which requires knowledge of the source location, the methods proposed in this study can be trained to estimate noise levels without knowledge of the source location. The accuracy of each model is assessed with the root-mean-square-error, and we discuss the practical implications of implementing such approaches in real-time systems.

Simultaneous estimation of cross-validation errors in least squares collocation applied for statistical testing and evaluation of the noise variance components

The cross-validation technique is a popular method to assess and improve the quality of prediction by least squares collocation (LSC). We present a formula for direct estimation of the vector of cross-validation errors (CVEs) in LSC which is much faster than element-wise CVE computation. We show that a quadratic form of CVEs follows Chi-squared distribution. Furthermore, a posteriori noise variance factor is derived by the quadratic form of CVEs. In order to detect blunders in the observations, estimated standardized CVE is proposed as the test statistic which can be applied when noise variances are known or unknown. We use LSC together with the methods proposed in this research for interpolation of crustal subsidence in the northern coast of the Gulf of Mexico. The results show that after detection and removing outliers, the root mean square (RMS) of CVEs and estimated noise standard deviation are reduced about 51 and 59%, respectively. In addition, RMS of LSC prediction error at data points and RMS of estimated noise of observations are decreased by 39 and 67%, respectively. However, RMS of LSC prediction error on a regular grid of interpolation points covering the area is only reduced about 4% which is a consequence of sparse distribution of data points for this case study. The influence of gross errors on LSC prediction results is also investigated by lower cutoff CVEs. It is indicated that after elimination of outliers, RMS of this type of errors is also reduced by 19.5% for a 5 km radius of vicinity. We propose a method using standardized CVEs for classification of dataset into three groups with presumed different noise variances. The noise variance components for each of the groups are estimated using restricted maximum-likelihood method via Fisher scoring technique. Finally, LSC assessment measures were computed for the estimated heterogeneous noise variance model and compared with those of the homogeneous model. The advantage of the proposed method is the reduction in estimated noise levels for those groups with the fewer number of noisy data points.

Fast noise level estimation algorithm based on principal component analysis transform and nonlinear rectification

We proposed a noniterative principal component analysis (PCA)-based noise level estimation (NLE) algorithm that addresses the problem of estimating the noise level with a two-step scheme. First, we randomly extracted a number of raw patches from a given noisy image and took the smallest eigenvalue of the covariance matrix of the raw patches as the preliminary estimation of the noise level. Next, the final estimation was directly obtained with a nonlinear mapping (rectification) function that was trained on some representative noisy images corrupted with different known noise levels. Compared with the state-of-art NLE algorithms, the experiment results show that the proposed NLE algorithm can reliably infer the noise level and has robust performance over a wide range of image contents and noise levels, showing a good compromise between speed and accuracy in general.

Online Active Learning in Data Stream Regression Using Uncertainty Sampling Based on Evolving Generalized Fuzzy Models

In this paper, we propose three criteria for efficient sample selection in case of data stream regression problems within an online active learning context. The selection becomes important whenever the target values, which guide the update of the regressors as well as the implicit model structures, are costly or time-consuming to measure and also in case when very fast models updates are required to cope with stream mining real-time demands. Reducing the selected samples as much as possible while keeping the predictive accuracy of the models on a high level is, thus, a central challenge. This should be ideally achieved in unsupervised and single-pass manner. Our selection criteria rely on three aspects: 1) the extrapolation degree combined with the model's nonlinearity degree , which is measured in terms of a new specific homogeneity criterion among adjacent local approximators; 2) the uncertainty in model outputs, which can be measured in terms of confidence intervals using so-called adaptive local error bars — we integrate a weighted localization of an incremental noise level estimator and propose formulas for online merging of local error bars; 3) the uncertainty in model parameters, which is estimated by the so-called A-optimality criterion, which relies on the Fisher information matrix. The selection criteria are developed in combination with evolving generalized Takagi–Sugeno (TS) fuzzy models (containing rules in arbitrarily rotated position), as it could be shown in previous publications that these outperform conventional evolving TS models (containing axis-parallel rules). The results based on three high-dimensional real-world streaming problems show that a model update based on only 10%–20% selected samples can still achieve similar accumulated model errors over time to the case when performing a full model update on all samples. This can be achieved with a negligible sensitivity on the size of the active learning latency buffer. Random sampling with the same percentages of samples selected, however, achieved much higher error rates. Hence, the intelligence in our sample selection concept leads to an economic balance between model accuracy and measurement as well computational costs for model updates.

Urban noise mapping with a crowd sensing system

Noise pollution poses a serious threat to people living in cities today. To alleviate the negative impact of noise pollution, an urban noise mapping can be helpful. In this paper, we present the design of NoiseSense, a crowd sensing system for housing a real-time urban noise mapping service. A major challenge in building such a system is caused by the sparsity problem of the limited noise measurement data from smartphones. To tackle this challenge, we propose a hybrid approach including a neighborhood-based noise level estimation method and a semi-supervised tensor completion algorithm for inferring noise levels for locations without measurements by smartphone users. This approach leverages a variety of urban data sources, such as Point of Interests, road networks, and check-in data. We also provide a noise prediction method for forecasting the noise levels in the next few hours. We implemented the system and developed an APP for smartphone users. We conducted experiments and field study. The experimental results show that the proposed approach is superior in inferring noise levels merely with sparse measurements from smartphone users. And the prediction approach also outperforms other baseline methods.

Adaptive SVD Domain-Based White Gaussian Noise Level Estimation in Images

Noise level estimation is a challenging area of digital image processing with a variety of applications, including image enhancement, image segmentation, and feature extraction. In this paper, an adaptive estimation of additive white Gaussian noise level based on the singular value decomposition (SVD) of images is proposed. The proposed algorithm aims to improve the performance of noise level estimation in the SVD domain at low noise levels. An initial noise level estimate is used to adjust the parameters of the algorithm in order to increase the accuracy of noise level estimation. The proposed algorithm exhibits the ability to adapt the number of considered singular values and to accordingly adjust the slope of a linear function that describes how the average value of the singular value tail varies with noise levels. Although, for each image, the proposed algorithm performs the noise level estimation twice in two distinct stages, the singular value decompositions are only performed in the first stage of the algorithm. The experimental results demonstrate that the proposed algorithm improves the noise level estimation at low noise levels without a significant increase in computational complexity. At noise level $\sigma = 15$ , the improvements in the mean square level are about 39% at the expense of slightly higher additional computational time.

AIRCRAFT ENVIRONMENTAL NOISE LEVEL ESTIMATION AT LANDING APPROACH

Three approximate methods are proposed for the estimated noise level of an aircraft performing approach. The noise level from the power plant is determined using existing software packages. In the first two methods, the estimation of the airframe noise level is based on modern concepts of the ratio of the acoustic noise emission from the power plant and that of the aircraft airframe, or on the known data on the relationship between the noise emissions from the chassis and the high lift devices, and the chassis noise level is calculated using known semi-empirical methods. In the third method, to estimate aircraft noise it is proposed to use experimental data on the statistically minimum environmental noise level at landing approach of an airplane with a conventional airframe layout.

Fine-scale movement responses of free-ranging harbour porpoises to capture, tagging and short-term noise pulses from a single airgun.

Knowledge about the impact of anthropogenic disturbances on the behavioural responses of cetaceans is constrained by lack of data on fine-scale movements of individuals. We equipped five free-ranging harbour porpoises (Phocoena phocoena) with high-resolution location and dive loggers and exposed them to a single 10 inch3 underwater airgun producing high-intensity noise pulses (2–3 s intervals) for 1 min. All five porpoises responded to capture and tagging with longer, faster and more directed movements as well as with shorter, shallower, less wiggly dives immediately after release, with natural behaviour resumed in less than or equal to 24 h. When we exposed porpoises to airgun pulses at ranges of 420–690 m with noise level estimates of 135–147 dB re 1 µPa2s (sound exposure level), one individual displayed rapid and directed movements away from the exposure site and two individuals used shorter and shallower dives compared to natural behaviour immediately after exposure. Noise-induced movement typically lasted for less than or equal to 8 h with an additional 24 h recovery period until natural behaviour was resumed. The remaining individuals did not show any quantifiable responses to the noise exposure. Changes in natural behaviour following anthropogenic disturbances may reduce feeding opportunities, and evaluating potential population-level consequences should be a priority research area.

Probabilistic Modelling of the Temporal Variability of Urban Sound Levels

Relying on monitoring networks to compute or improve noise maps is an increasingly used approach. To be able to use this approach to provide adequate temporal treatments, a good understanding of the temporal variations within urban sound level time series is required. This paper provides an in-depth statistical analysis of the temporal characteristics of urban sound environments, on the basis of a wide measurement campaign during 8 month, at 23 measurement stations in Paris, which cover a large variety of urban sound environments. The time series of sound levels were recorded continuously with a 125 ms-time resolution, from which LA(50,1h) values were extracted. In total, 72 time-slots of interest are defined (24 1h-periods covering all days of the week). The statistical analysis determines for each station the Daily Average Noise Pattern (DANP), and for each of the 72 time-slots the 1h-Generalized Extreme Values distributions. The Generalized Extreme Values distributions are found to outperform the normal distributions to model the LA(50,1h) distributions. In addition, the average sound level differences between these 72 1h-time periods are calculated along with their variability, resulting in 72x72 delta matrices that describe the temporal relations between sound levels. This database is then used to develop two models, which aim to estimate DANP based on a limited amount of measurements. The model M1 relies on the delta matrices, whereas the model M2 consists of a weighted average of the DANP that are stored in the database in which the weights are based upon measures of similarity between the stations. Both models rely on probability density functions, and provide a measure for the reliability of the estimated noise levels. A test of both modelling approaches through simulated measurements shows that the model M1 seems to be more robust in case measurements are inaccurate. Beyond these two models, the proposed database could serve in the development of further models that aim to estimate sound levels based on a limited amount of measurements.

Focus and Blurriness Measure Using Reorganized DCT Coefficients for an Autofocus Application

In this paper, two metrics for measuring image sharpness are presented and used for an autofocus (AF) application. Both measures exploit reorganized discrete cosine transform (DCT) representation. The first metric is a focus measure, which involves optimal high- and middle-frequency coefficients to evaluate relative sharpness. It is robust to noise while remaining sensitive to the best focus position. A psychometric function-based metric is introduced to quantify the focus measure. The second metric is a no-reference blurriness metric, which is used to measure absolute blurriness. It first constructs multiscale DCT edge maps using directional energy information and then determines image blurriness by combining change information in edge structures with image contrast. This metric gives predictions that are closely correlated with subjective perceived scores and shows performance comparable with that of state-of-the-art methods, especially for noisy images. For noisy situations, the two metrics are adjusted adaptively according to the estimated noise level. To prevent the introduction of extra computational load, an efficient noise-level estimation algorithm based on median absolute deviation is presented. This algorithm exploits only the available reorganized DCT coefficients. With the focus and blurriness measures, an AF method for which the two metrics play an important role was developed. Because of their high-quality performance, the realized AF function is able to locate the best focus position swiftly and reliably.

Detail-Preserving Image Denoising via Adaptive Clustering and Progressive PCA Thresholding

This paper proposes a detail-preserving image denoising method via cluster-wise progressive principal component analysis (PCA) thresholding based on the Marchenko–Pastur (MP) law in random matrix theory. According to random matrix theory, an efficient and stable noise-level estimation method is also presented. Specifically, a global Gaussian noise level is estimated by interpreting the relationship between noise and eigenvalues of PCA for noisy patch matrices via the MP law in conjunction with the observation that vectors extracted from a noise-free image often lie in a low-dimensional subspace. Before noise removal, an adaptive clustering method is developed to automatically determine a suitable number of clusters segregating patches with different features (edges and textures). To denoise each cluster matrix, progressive PCA thresholding is performed. First, a hard thresholding of singular values in the singular value decomposition domain based on the MP law is applied to find a low-rank approximation to the cluster matrix. Second, the remaining noises of the low-rank matrix are further removed in the PCA transform domain using a special soft thresholding, i.e., the linear minimum mean-square-error technique with locally estimated parameters. The experiments show that the proposed method not only achieves state-of-the-art denoising performance in terms of quantitative indices, but also preserves visually important image details best.

Evaluation of Blur and Gaussian Noise Degradation in Images Using Statistical Model of Natural Scene and Perceptual Image Quality Measure

In this paper we present a new method for classification of image degradation type based on Riesz transform coefficients and Blind/Referenceless Image Spatial Quality Evaluator (BRISQUE) that employs spatial coefficients. In our method we use additional statistical parameters that give statistically better results for blur and all tested degradations together in comparison with previous methods. A new method to determine level of blur and Gaussian noise degradation in images using statistical model of natural scene is presented. We defined parameters for evaluation of level of Gaussian noise and blur degradation in images. In real world applications reference image is usually not available therefore the proposed method enables classification of image degradation by type and estimation of Gaussian noise and blur levels for any degraded image.

An automatic glucose monitoring signal denoising method with noise level estimation and responsive filter updating

Abstract Although continuous glucose monitoring (CGM) devices have been the crucial part of the artificial pancreas, their success has been discounted by random measurement noise. The difficulty of denoising methods for CGM is that the filter parameters are hard to be determined to well reflect the internal blood glucose dynamics and the real noise level. Besides, the noise level may change from device to device, subject to subject and also within the subject as time goes on which thus requires that the filter parameters should be adjusted to follow the noise changes. In this paper, we proposed an automatic CGM signal denoising method which covers three important components. First, the state transition matrix which reveals the internal blood glucose dynamics and plays an important role in determining filter parameters can be estimated in response to different patients. Second, the real noise level can be estimated which are used to set the values of filter parameters properly. Third, a responsive filter updating rule is developed which can judge whether the values of filter parameters should be updated in response to the variability of signal-to-noise ratio. The process of dealing with the CGM signals is executing as follows: the model parameters and the noise level are evaluated using Expectation Maximization (EM) algorithm which can fix proper filter parameters for the current signals. Then, a confidence interval is defined by computing the power spectral density (PSD) of the CGM signals to identify the changes of noise level which can tell whether or not the parameters of Kalman filter (KF) should be adjusted. The above issues are investigated based on thirty in silico subjects and ten clinical subjects. The proposed method can work well to identify the changes of noise level and determine proper filter parameters.

Automatic Hyperspectral Image Restoration Using Sparse and Low-Rank Modeling

Hyperspectral restoration is a preprocessing step for hyperspectral imagery. In this letter, we propose a parameter-free method for the restoration of hyperspectral images (HSIs) called HyRes. The restoration method is based on a sparse low-rank model that uses the $\ell _{1}$ penalized least squares for estimating the unknown signal. The Stein’s unbiased risk estimator is exploited to select all the parameters of the model yielding a fully automatic (parameter free) technique. Experimental results confirm that HyRes outperforms the state-of-the-art techniques in terms of signal-to-noise ratio, structural similarity index, and spectral angle distance for a simulated data set and in terms of noise-level estimation for the real data sets used in this letter. In the experiments, it was noted that HyRes is computationally less expensive compared with competitive techniques. Therefore, HyRes can be used as a reliable automatic preprocessing step for further analysis of HSIs.

Data correlation based noise level estimation for cone beam projection data.

In regularized iterative reconstruction algorithms, the selection of regularization parameter depends on the noise level of cone beam projection data. Our aim is to propose an algorithm to estimate the noise level of cone beam projection data. We first derived the data correlation of cone beam projection data in the Fourier domain, based on which, the signal and the noise were decoupled. Then the noise was extracted and averaged for estimation. An adaptive regularization parameter selection strategy was introduced based on the estimated noise level. Simulation and real data studies were conducted for performance validation. There exists an approximately zero-energy double-wedge area in the 3D Fourier domain of cone beam projection data. As for the noise level estimation results, the averaged relative errors of the proposed algorithm in the analytical/MC/spotlight-mode simulation experiments were 0.8%, 0.14% and 0.24%, respectively, and outperformed the homogeneous area based as well as the transformation based algorithms. Real studies indicated that the estimated noise levels were inversely proportional to the exposure levels, i.e., the slopes in the log-log plot were -1.0197 and -1.049 with respect to the short-scan and half-fan modes. The introduced regularization parameter selection strategy could deliver promising reconstructed image qualities. Based on the data correlation of cone beam projection data in Fourier domain, the proposed algorithm could estimate the noise level of cone beam projection data accurately and robustly. The estimated noise level could be used to adaptively select the regularization parameter.

Novel scaling law for estimating propeller tip vortex cavitation noise from model experiment

The tip vortex cavitation (TVC) noise of marine propellers is of interest due to the environmental impacts from commercial ships as well as for the survivability of naval ships. Due to complicated flow and noise field around a marine propeller, a theoretical approach to the estimation of TVC noise is practically unrealizable. Thus, estimation of prototype TVC noise level is realized through extrapolation of the model TVC noise level measured in a cavitation tunnel. In this study, for the prediction of prototype TVC noise level from a model test, a novel scaling law reflecting the physical basis of TVC is derived from the Rayleigh-Plesset equation, the Rankine vortex model, the lifting surface theory, and other physical assumptions. Model and prototype noise data were provided by Samsung Heavy Industries (SHI) for verification. In applying the novel scaling law, similitude of the spectra of nuclei is applied to assume the same nuclei distribution in the tip vortex line of the model and the prototype. It was found that the prototype TVC noise level predicted by the novel scaling law has better agreement with the prototype TVC noise measurement than the prototype TVC noise level predicted by the modified ITTC noise estimation rule.

Sparse Unmixing of Hyperspectral Data with Noise Level Estimation

Recently, sparse unmixing has received particular attention in the analysis of hyperspectral images (HSIs). However, traditional sparse unmixing ignores the different noise levels in different bands of HSIs, making such methods sensitive to different noise levels. To overcome this problem, the noise levels at different bands are assumed to be different in this paper, and a general sparse unmixing method based on noise level estimation (SU-NLE) under the sparse regression framework is proposed. First, the noise in each band is estimated on the basis of the multiple regression theory in hyperspectral applications, given that neighboring spectral bands are usually highly correlated. Second, the noise weighting matrix can be obtained from the estimated noise. Third, the noise weighting matrix is integrated into the sparse regression unmixing framework, which can alleviate the impact of different noise levels at different bands. Finally, the proposed SU-NLE is solved by the alternative direction method of multipliers. Experiments on synthetic datasets show that the signal-to-reconstruction error of the proposed SU-NLE is considerably higher than those of the corresponding traditional sparse regression unmixing methods without noise level estimation, which demonstrates the efficiency of integrating noise level estimation into the sparse regression unmixing framework. The proposed SU-NLE also shows promising results in real HSIs.

A Multiple Image-Based Noise Level Estimation Algorithm

In this letter, a novel multiple image-based Gaussian noise level estimation (NLE) algorithm for natural images by jointly exploiting the noise level-aware feature extraction and the local means (LM) estimation techniques was proposed. We employed some efficient and powerful noise level-aware features in the form of a feature vector to characterize the noise levels across image contents. Based on this, we adopted LM estimation scheme to estimate the noise level for an image to be estimated by comparing multiple images of similar noise levels in a preconstructed sample database. We had verified the accuracy and efficiency of the proposed NLE algorithm on a large of images from several benchmark databases. Compared with the competing NLE algorithms, our algorithm is superior to them for noise level estimation in terms of both estimation accuracy and execution time.

Annual traffic noise levels estimation based on temporal stratification

This paper proposes a temporal sampling strategy that increases the accuracy of long-term noise level estimation and allows to establish the estimation error according to the number of sampled days. Days of the week are stratified into working days and weekend days. This research shows how to use measurements of Leq on working days to estimate the corresponding values for weekend days. This is possible because working days have higher noise levels and less variability than weekend days. The improvement in accuracy allows for a reduction in the number of required sampled days compared to taking samples randomly, which would help to reduce the uncertainty in environmental noise assessment. As a reference, to obtain a 90% confidence interval of ±1 dB for Lday, the proposed sampling strategy reduces the required measurement days by more than 38%. For LDEN, the reduction is close to 18% of the total number of days. The proposed strategy could be adapted to different environments by simply changing a few parameters.