Noise Variance Estimation Research Articles

Parameter and uncertainty estimation in stochastic differential equation models with multi-rate data and nonstationary disturbances

Updated methods are proposed for estimating model parameters and error-covariance matrices in stochastic differential equation (SDE) models. New expressions, based on the LAMLE (Laplace Approximation Maximum Likelihood Estimation) and LAB (Laplace Approximation Bayesian) SDE estimation methods are derived so that LAMLE and LAB can be used for systems with multi-rate data and nonstationary disturbances. The updated LAMLE method is tested using simulated data from a two-state continuous stirred tank reactor (CSTR) model. Comparisons are made with the results obtained using the continuous-time stochastic method (CTSM), confirming that the updated LAMLE algorithm provides reliable estimates for unknown model parameters, measurement noise variances, and process-error variances. In all situations tested, the updated LAMLE algorithm converged to reliable parameter and uncertainty estimates, while avoiding convergence difficulties encountered by CTSM in some situations. The updated LAMLE and LAB algorithms will be useful for parameter estimation in online models used in advanced process monitoring and control applications where multi-rate data and nonstationary disturbances are often encountered. Estimates of measurement noise variances and process-error variances will be helpful for state-estimator tuning.

An Energy Detection-Based Spectrum-Sensing Method for Cognitive Radio

Energy detection (ED) method is one of the most commonly used signal-sensing methods in spectrum sensing due to its low implementation complexity. ED can achieve good detection performance when the noise variance is known. However, in most cases, the noise variance is estimated, which may result in the uncertainty in noise variance. In the presence of noise variance uncertainty, the detection performance of the ED method may degrade significantly. To reduce the impact of uncertainty in noise variance, an ED-based sensing method is proposed in this paper. This method combines these signal samples sampled by multiple antennas to obtain the decision statistic as ED does. A novel technique is proposed to construct the decision threshold so that it is independent of the noise variance. As a consequence, the proposed method is free of the effect of noise variance uncertainty, and the noise variance estimation is not need. The simulation results show that the detection probability of this method can approach to 1 even when the SNR is −15 dB while the detection probability of ED is below 0.8, which means the detection performance of the proposed method can outperform the ED method without the noise variance estimation when the number of antennas is greater than two.

Iterative Detection for Orthogonal Time Frequency Space Modulation With Unitary Approximate Message Passing

The orthogonal-time-frequency-space (OTFS) modulation has emerged as a promising modulation scheme for high mobility wireless communications. To harvest the time and frequency diversity promised by OTFS, some promising detectors, especially message passing based ones, have been developed by taking advantage of the sparsity of the channel in the delay-Doppler domain. However, when the number of channel paths is relatively large or fractional Doppler shifts have to be considered, the complexity of existing detectors is a concern, and the existing message passing based detectors suffer from performance loss. In this work, we investigate the design of OTFS detectors based on the approximate message passing (AMP). In particular, leveraging the unitary AMP (UAMP), we design new detectors that enjoy the structure of the channel matrix and allow efficient implementation. In addition, the estimation of noise variance is incorporated into the UAMP-based detectors. Thanks to the robustness of UAMP relative to AMP, the UAMP-based detectors deliver superior performance, and outperform state-of-the-art detectors significantly. We also investigate iterative joint detection and decoding in a coded OTFS system, where the OTFS detectors are integrated into a powerful turbo receiver, leading to considerable performance gains.

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.

On the Signal-to-Noise Ratio Wall of Energy Detection in Spectrum Sensing

In this paper, a comprehensive analysis of the signal-to-noise ratio wall (SNRw) of cognitive radio (CR)-based non-cooperative spectrum sensing (nCSS) and cooperative spectrum sensing (CSS) using energy detection (ED) is presented. The analysis considers a novel realistic noise uncertainty (NU) model in which it is assumed that the estimated noise variance used to determine the decision threshold is unbiased and follows a truncated-Gaussian random distribution with configurable limits. Expressions are derived for the individual detection performances at CRs and global detection performances at the fusion center in terms of probability of false alarm and probability of detection and the SNRw of ED in nCSS and CSS in hard-decision fusion under the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k $ </tex-math></inline-formula> -out-of- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M $ </tex-math></inline-formula> rule, and soft-decision fusion, considering the proposed NU model, respectively. Empirical SNRw algorithms are also proposed, allowing for the SNRw computation of any detector, including the ED, in nCSS and CSS. All theoretical findings are verified through computer simulations or empirical results.

Mixed Noise Estimation for Hyperspectral Image Based on Multiple Bands Prediction

The noise in hyperspectral images (HSIs) is mixed with signal-independent (SI) thermal noise and signal-dependent (SD) photon noise. In this letter, a mixed noise estimation algorithm is proposed to estimate the noise level of SI and SD noise, respectively. The proposed algorithm removes the spectral correlation of the HSI by multiple linear regression (MLR) on several neighboring bands. According to the relationship between the prediction coefficients by MLR and the local statistics, an overdetermined equation system with respect to the variances of the SI and SD noise is established. Then the estimated noise variances are solved by the least-squares (LS) method. To ensure the accuracy of local statistics, regional clustering-based spatial preprocessing (RCSP) for HSI superpixel segmentation is employed to detect the homogeneous region. Experimental results on the simulated data confirm considerable improvements, and the real-life data experiment is implemented to validate the performance of the proposed algorithm.

Joint Parameter Estimation From Binary Observations Over Decentralized Channels

In wireless sensor networks, due to the bandwidth constraint, the distributed nodes (DNs) might only provide binary representatives of the source signal, and then transmit them to the central node (CN). In this paper, we consider the joint estimation of signal amplitude and background noise variance from binary observations over decentralized channels. We first analyze the Cram&#x00E9;r&#x2013;Rao lower bounds (CRLBs) of the parameters of interest and develop a quasilinear estimator (QLE), in which the desirable estimates can be obtained from several intermediate parameters linearly. Next, we consider a more realistic situation where the decentralized channel is noisy during the data transmission. Based on the error propagation model, the asymptotic analysis shows that the performance of the proposed QLE is mainly dominated by the thresholds of the quantizers, which encourages us to adopt a correlated quantization (CQ) scheme by exploiting the spatial correlation among background noises/channel noises. To ease the implementation of QLE in practice, an adaptive quantization (AQ) scheme is also proposed so as to obtain reasonable selections of the required thresholds. Finally, numerical simulations are provided to validate our theoretical findings.

A Blind SAR Image Despeckling Method Based on Improved Weighted Nuclear Norm Minimization

Coherent imaging of synthetic aperture radar (SAR) systems generates multiplicative speckle noise, severely impairs SAR images’ interpretability. Although numerous despeckling methods have been proposed over the past three decades, SAR despeckling remains an unsolved problem due to its uniqueness and complexity. To address these issues, we propose a novel SAR image despeckling method based on the framework of weighted nuclear norm minimization (WNNM). First, a Gaussian function is used to approximate the distribution of good similar patches (GSP). Clustering is then used to select the optimal patches for the GSP matrix. WNNM can then estimate the underlying clean component of the GSP matrix. To increase the speed of the WNNM, a modified version of the singular value decomposition (SVD) is introduced. Additionally, we developed a noise variance estimation method that enables blind despeckling with the proposed method. Extensive experimental results demonstrate that the proposed method yields superior objective indices and subjective visual inspection.

Retracted] Research on Fast Compensation Algorithm for Interframe Motion of Multimedia Video Based on Manhattan Distance

To improve the video quality, aiming at the problems of low peak signal‐to‐noise ratio, poor visual effect, and low bit rate of traditional methods, this paper proposes a fast compensation algorithm for the interframe motion of multimedia video based on Manhattan distance. The absolute median difference based on wavelet transform is used to estimate the multimedia video noise. According to the Gaussian noise variance estimation result, the active noise mixing forensics algorithm is used to preprocess the original video for noise mixing, and the fuzzy C‐means clustering method is used to smoothly process the noisy multimedia video and obtain significant information from the multimedia video. The block‐based motion idea is to divide each frame of the video sequence into nonoverlapping macroblocks, find the best position of the block corresponding to the current frame in the reference frame according to the specific search range and specific rules, and obtain the relative Manhattan distance between the current frame and the background of multimedia video using the Manhattan distance calculation formula. Then, the motion between the multimedia video frames is compensated. The experimental results show that the algorithm in this paper has a high peak signal‐to‐noise ratio and a high bit rate, which effectively improves the visual effect of the video.

A Novel Gaussian-Copula modeling for image despeckling in the shearlet domain

Image denoising, degraded by speckle noise, has turned into a prevalent problem in image processing. Speckle noise provides a granular perspective into the image and makes it difficult to have a clear interpretation of the singular and non-singular points. This paper proposes a novel statistical approach based on Gaussian Copula modeling in the Shearlet domain. The proposed multi-dimensional Minimum Mean Square Error (MMSE) processor consists of two key components. First, Bi Parameter Cauchy Gaussian Mixture model (BCGM) as the marginal distribution of shearlet coefficients is employed. Second, the joint-prior distribution modeling is formed, based on proposing the Gaussian copula, to model the dependency of the target coefficient respect to its neighbors. The closed form mathematical expression of proposed multi dimensional MMSE processor has some computational advantages, such as parallel computing. It will be shown that the proposed processor has adaptive behavior, meaning that, working non-linearly according to the estimated noise variance on each scale and direction of the shratlet transform. This behavior confirms that the designed processor is not sensitive to initial parameter settings, unlike the state-of-the-art filters in this area.

Parameter selection for CLAHE using multi-objective cuckoo search algorithm for image contrast enhancement

Contrast enhancement techniques that are proposed in the literature are devised to enhance image quality so as to provide better details for different image processing tasks. Histogram Equalization (HE) is a widely exploited technique to enhance contrast of the images. Histograms are used to measure the frequency of intensity levels in an image. The objective of HE is to distribute the intensity values in an image such that the lower contrast areas can gain higher contrast. HE techniques can be global or local. The Contrast Limited Adaptive Histogram Equalization (CLAHE) is a local HE method. Thus, CLAHE can handle the problems of the classical HE algorithm. CLAHE employs two parameters, which are, respectively, number of tiles and clip limit. The efficiency of the CLAHE depends on these two parameters. Hence, the results can be changed if the parameters of the CLAHE is adjusted. The value of the optimal parameters can vary according to the image type. In this paper, Multi-objective Cuckoo Search (MOCS) is employed to determine optimal parameters for CLAHE to enhance the contrast of images. For MOCS, first fitness function is set for computing Entropy and second fitness function is set for computing Fast Noise Variance Estimation (FNVE) so as to provide a good local detail preservation and prevent noise amplification in the output image. Image dataset is taken from Contrast Enhancement Evaluation Database (CEED2016), which can be found in Mendeley data repository. This database is used for evaluating the overall performance of the proposed method. Evaluation results of the proposed method are given in terms of Absolute Mean Brightness Error (AMBE), Peak Signal-to-noise Ratio (PSNR), Mean Squared Error (MSE), Maximum Difference (MD), Mean Absolute Error (MAE) and Computing Time (CT) .

Noise estimation in single coil MR images

Magnetic resonance (MR) signal is degraded by acquisition noise. Estimation and removal of noise from MR images is essential for analysis and further pre-processing. The work proposes a new method for noise variance estimation in single coil magnitude MR images. The proposed noise estimator is derived using the Maximum Á Posterior (MAP) estimator. Noise follows a Gaussian distribution at high Signal to Noise (SNR) ratio and Rician distribution at low SNR. In the MAP framework, Gaussian noise model and local statistics of the noisy image are instrumental in estimation of noise at high SNR. The proposed work also exploits the local second order moments in the MAP framework for noise estimation at low SNR. Convergence of the proposed MAP framework further highlights the optimal performance of the noise estimator. Noise estimation experiments conducted on Brainweb database exhibit encouraging performance at high as well as low SNR.

Underdetermined Estimation of Multiple Parameters for Partially Polarized Signals With Dual-Polarized Coprime Array

This letter considers the problem of underdetermined estimation of direction-of-arrival (DOA) and polarization parameters, including the degree of polarization (DOP), polarization orientation angle (POA), and polarization ellipticity angle (PEA), for partially polarized (PP) signals with a dual-polarized coprime array. Firstly, the increased dimension due to dual-polarized sensors is reduced by adding two covariance matrices, which facilitates the coarray construction. Then, the holes in the coarray of coprime array are interpolated via utilizing the annihilating relation. At last, the DOAs and array noise variance are obtained by solving an annihilating relation based optimization problem and then used to reconstruct the coherency matrices via the weight least squares (WLS). The polarization parameters can be estimated by performing eigendecomposition on the reconstructed coherency matrices. We show the underdetermined estimation of array noise variance which is difficult for conventional methods is vital for accurate underdetermined estimation of the polarization parameters. The performances of the proposed method are verified by numerical simulations and compared with other representative methods including the Cramer-Rao bound (CRB).

A novel bias compensation recursive least square‐multiple weighted dual extended Kalman filtering method for accurate state‐of‐charge and state‐of‐health co‐estimation of lithium‐ion batteries

AbstractState‐of‐charge and state‐of‐health of power lithium‐ion batteries are two important state parameters for battery management system monitoring. To accurately estimate the state‐of‐charge and state‐of‐health of in real time, the ternary lithium‐ion battery is taken as the research object, and a novel bias compensation recursive least square‐multiple weighted dual extended Kalman filtering method is proposed innovatively. The noise variance estimation is introduced to compensate the parameters identified by the general least square method to realize the accurate identification. The estimation value is corrected by using the residual and Kalman gain at multiple times, and different weights are configured for each residual according to the amount of information contained. The data of different complex conditions are used to verify the feasibility of the proposed algorithm, the results show that the root‐mean‐square error of bias compensation recursive least square‐multiple weighted dual extended Kalman filtering under dynamic stress test and Beijing bus dynamic stress test condition can be controlled within 1.62% and 2.70% in state‐of‐charge estimation, 0.17% and 0.81% in state‐of‐health estimation, which verifies that the proposed algorithm in this research has good running effect. The novel bias compensation recursive least square‐multiple weighted dual extended Kalman filtering method lays a theoretical foundation for the safe operation of electric vehicles.

Density deconvolution with Laplace errors and unknown variance

We consider density deconvolution with zero-mean Laplace noise in the context of an error component regression model. We adapt the minimax deconvolution methods of Meister (2006) to allow estimation of the unknown noise variance. We propose a semi-uniformly consistent estimator for an ordinary-smooth target density and a modified "variance truncation device” for the unknown noise variance. We provide a simulation study and practical guidance for the choice of smoothness parameters of the ordinary-smooth target density. We apply restricted versions of our estimator to a stochastic frontier model of US banks and to a measurement error model of daily saturated fat intake.

An assessment of noise variance estimations in Bayes threshold denoising under stationary wavelet domain on brain lesions and tumor MRIs

PurposeA major key success factor regarding proficient Bayes threshold denoising refers to noise variance estimation. This paper focuses on assessing different noise variance estimations in three Bayes threshold models on two different characteristic brain lesions/tumor magnetic resonance imaging (MRIs).Design/methodology/approachHere, three Bayes threshold denoising models based on different noise variance estimations under the stationary wavelet transforms (SWT) domain are mainly assessed, compared to state-of-the-art non-local means (NLMs). Each of those three models, namely D1, GB and DR models, respectively, depends on the most detail wavelet subband at the first resolution level, on the entirely global detail subbands and on the detail subband in each direction/resolution. Explicit and implicit denoising performance are consecutively assessed by threshold denoising and segmentation identification results.FindingsImplicit performance assessment points the first–second best accuracy, 0.9181 and 0.9048 Dice similarity coefficient (Dice), sequentially yielded by GB and DR; reliability is indicated by 45.66% Dice dropping of DR, compared against 53.38, 61.03 and 35.48% of D1 GB and NLMs, when increasing 0.2 to 0.9 noise level on brain lesions MRI. For brain tumor MRI under 0.2 noise level, it denotes the best accuracy of 0.9592 Dice, resulted by DR; however, 8.09% Dice dropping of DR, relative to 6.72%, 8.85 and 39.36% of D1, GB and NLMs is denoted. The lowest explicit and implicit denoising performances of NLMs are obviously pointed.Research limitations/implicationsA future improvement of denoising performance possibly refers to creating a semi-supervised denoising conjunction model. Such model utilizes the denoised MRIs, resulted by DR and D1 thresholding model as uncorrupted image version along with the noisy MRIs, representing corrupted version ones during autoencoder training phase, to reconstruct the original clean image.Practical implicationsThis paper should be of interest to readers in the areas of technologies of computing and information science, including data science and applications, computational health informatics, especially applied as a decision support tool for medical image processing.Originality/valueIn most cases, DR and D1 provide the first–second best implicit performances in terms of accuracy and reliability on both simulated, low-detail small-size region-of-interest (ROI) brain lesions and realistic, high-detail large-size ROI brain tumor MRIs.

Deep noise estimation and removal for real-world noisy images

This paper proposes a joint noise estimation and removal network for real-world noisy images. We observe that the noise variance depends on the image intensity and the variances of neighboring pixels are not similar due to the demosaicing interpolation. Therefore, for noise estimation, we propose to pack each 2 × 2 noisy block into a 4D vector as the input of the noise level estimation network, which makes the noise variances of adjacent pixels to be similar. This strategy not only reduces the computational complexity but also improves the estimation accuracy. For noise removal, we propose to concatenate the estimated noise variance with the noisy image as the input of the noise removal network, which takes advantages of the correlations between noise levels and image intensities. In addition, we propose a RSD (Residual SE D-Conv) block, which explores the spatial and channel correlations of realistic noise. Considering the realistic noisy and clean image pairs are limited for training, we utilize synthetic noisy images to train the network first and then fine tune the network with real images. Experimental results demonstrate that the proposed method outperforms competing methods for both noise estimation and removal tasks.

Adaptive robust estimation in sparse vector model

For the sparse vector model, we consider estimation of the target vector, of its ℓ2-norm and of the noise variance. We construct adaptive estimators and establish the optimal rates of adaptive estimation when adaptation is considered with respect to the triplet “noise level—noise distribution—sparsity.” We consider classes of noise distributions with polynomially and exponentially decreasing tails as well as the case of Gaussian noise. The obtained rates turn out to be different from the minimax nonadaptive rates when the triplet is known. A crucial issue is the ignorance of the noise variance. Moreover, knowing or not knowing the noise distribution can also influence the rate. For example, the rates of estimation of the noise variance can differ depending on whether the noise is Gaussian or sub-Gaussian without a precise knowledge of the distribution. Estimation of noise variance in our setting can be viewed as an adaptive variant of robust estimation of scale in the contamination model, where instead of fixing the “nominal” distribution in advance we assume that it belongs to some class of distributions.

Rapid Blind Denoising Method for Grating Fringe Images Based on Noise Level Estimation

Object profile measurement theory and technology based on grating fringe image projection are popular topics of research. However, due to the presence of noise, the phase extracted from captured grating fringe images may be wrong, affecting the measurement results. To manage noise with unknown intensity levels, we use Gaussian distribution to model the noise, and propose a novel rapid blind denoising method. First, we establish an energy expression model for grating fringe images. After performing singular value decomposition (SVD) on the grating fringe image, we establish a linear relationship between the average energy of the image and the noise variance. Second, we propose a noise variance estimation method based on a single frame grating fringe image. By adding an auxiliary image of zero-mean Gaussian noise, we can obtain the estimated noise variance. Third, a Gaussian filtering method of the phase maps using the estimated variance, is employed to reduces the amount of data processing. The experimental results show that the proposed method can complete noise processing faster than five other methods, and extract the phase profile of two measured models with minimum root-mean-square (RMS) error of 0.0686 and 0.0673 rad.

Maximum-Likelihood, Magnitude-Based, Amplitude and Noise Variance Estimation

Maximum likelihood (ML) amplitude and noise variance estimation without having to jointly estimate the frequency and the phase and based only on information from the noisy received signal magnitude, is studied for a single sinusoid in complex additive white Gaussian noise. This estimation problem is equivalent to the classic problem of parameter estimation for the Rician distribution. While solving the likelihood equation is impossible in general, we propose a new approach based on a large argument approximation. For the case with known noise variance, a closed-form ML amplitude estimator is obtained, which outperforms the conventional root-mean-square estimator. For the case with unknown noise variance, the closed-form joint amplitude and noise variance estimators obtained do not require prior knowledge of one another.