Noise Variance Estimation Research Articles

A unified message-passing algorithm for MIMO-SDMA in software-defined radio

This paper presents a novel software radio implementation for joint channel estimation, data decoding, and noise variance estimation in multiple-input multiple-output (MIMO) space division multiple access (SDMA). In contrast to many other iterative solutions, the proposed receiver is derived within the theoretical framework of a unified message-passing algorithm, combining belief propagation (BP) and the mean field approximation (MF) on the corresponding factor graph. The algorithm minimizes the region-based variational free energy in the system under appropriate conditions and, hence, converges to a fixpoint. As a use-case, we consider the high-rate packet-oriented IEEE 802.11n standard. Our receiver is implemented on a software-defined radio platform dubbed MIMONet, composed of a GNU radio software component and a universal software radio peripheral (USRP). The receiver was evaluated in real indoor environments. The results of our study clearly show that, once synchronization issues are properly addressed, the BP-MF receiver provides a substantial performance improvement compared to a conventional receiver also in real-world settings. Such improvement comes at the expense of an increase in running time that can be as high as 87. Therefore, the trade-off between communication performance and receiver complexity should be carefully evaluated in practical settings.

Noise variance estimation for Kalman filter

In this paper, we propose an algorithm that evaluates noise variance with a numerical integration method. For noise variance estimation, we use Krogh method with a variable integration step. In line with common practice, we limit our study to fourth-order method. First, we perform simulation tests for randomly generated signals, related to the transition state and steady state. Next, we formulate three methodologies (research hypotheses) of noise variance estimation, and then compare their efficiency.

New methods to estimate the observed noise variance for an ARMA model

Abstract For an ARMA model with an observed noise, the observed noise variance estimation is not only a part of the model identification, but also its estimation accuracy affects the following MA parameter estimation accuracy directly. However, it is difficult to improve the estimation accuracy of the observed noise variance, especially when the observed noise variance is small. In this paper, two new methods are proposed to estimate the observed noise variance accurately. In the first method, the lower lags of the auto-covariance function are used to estimate the observed noise variance with high estimation accuracy, but it is valid only when the AR order is greater than the MA order. In the second method, the ARMA model is approximated as a high-order AR model so that it is effective even though the AR order is equal to or less than the MA order. If the observed noise variance is too small, its estimation error may be too large to valid the estimate. An empirical criterion is proposed to judge the necessity of estimating the observed noise variance. The proposed methods are verified by simulations and applied to the random noise modeling for gyroscopes tentatively.

Single Snapshot Detection and Estimation of Reflections From Room Impulse Responses in the Spherical Harmonic Domain

We study the detection and estimation of the parameters related to the deterministic model of the reflections of room impulse responses measured with a spherical microphone array. More specifically, we investigate the problem of detecting and estimating several reflections of a single snapshot of data in the spherical harmonic (SH) domain with four detection and four estimation methods, presented previously in the array processing research. Three of the estimation methods are based on Bayesian Maximum a Posteriori (MAP) estimation, and they employ a prior normal distribution on the signals. The estimation methods are compared with the deterministic maximum likelihood (DML) method [Tervo & Politis 2015]. In the detection task, two information criteria-based methods, minimum description length (MDL) and Akaike information criteria (AIC), a normalized likelihood (NL) based method, and a Bayesian detection scheme (BDS) are explored. The experiments study the performance of the methods with simulated and real data experiments. The simulation results show that the MAP estimation methods have a lower root mean squared error (RMSE) than DML in the reflection signal amplitude estimation, but all three have similar performance in the direction of arrival (DOA) and noise variance estimation, although in general RMSE of DOA estimation of MAP methods is slightly lower that that of DML. In addition, in the detection task, the BDS and AIC are the most robust against additive noise, and NL and AIC have the best detection rate when more than two reflections are simulated. The results of the real data experiments show that all the estimation methods have similar performance for DOA and noise variance estimation, while the Bayesian MAP methods have a clearly lower RMSE for reflection signal amplitude estimation than DML. In total, NL has the highest detection rate in the real data experiments.

On estimating market microstructure noise variance

We study the market microstructure noise-variance estimation of high-frequency stock prices. Based on the Hansen and Lunde (2006) approach, we propose estimates using subsampling method at different time scales. We conduct a Monte Carlo study to compare our method against others in the literature. Our results show that our proposed estimates have lower (absolute) mean error and root mean-squared error, and their performance is quite stable at different time scales.

Frame timing estimation based on statistical analysis for orthogonal frequency division multiplexing systems in multipath fading channels

This study investigates the problem of frame timing estimation in orthogonal frequency division multiplexing systems. Conventional timing estimation methods, which take advantage of the correlation property of a given preamble, always experience performance degradation in multipath fading channels with severe channel dispersion. To achieve accurate timing estimation, the authors propose a robust threshold-based timing detection method independent of the preamble structure. Based on the autocorrelation and cross-correlation, a novel timing metric with an extended correlation length is proposed to mitigate noise and resist large carrier frequency offsets. Due to the superior statistical property of the proposed timing metric, the threshold can be easily determined with no need for the process of noise variance estimation. Simulation results under different multipath fading channels demonstrate that the proposed method achieves a remarkably improved timing accuracy compared to the existing methods.

Intelligent estimation of noise and blur variances using ANN for the restoration of ultrasound images.

Ultrasound (US) imaging is a widely used clinical diagnostic tool in medical imaging techniques. It is a comparatively safe, economical, painless, portable, and noninvasive real-time tool compared to the other imaging modalities. However, the image quality of US imaging is severely affected by the presence of speckle noise and blur during the acquisition process. In order to ensure a high-quality clinical diagnosis, US images must be restored by reducing their speckle noise and blur. In general, speckle noise is modeled as a multiplicative noise following a Rayleigh distribution and blur as a Gaussian function. Hereto, we propose an intelligent estimator based on artificial neural networks (ANNs) to estimate the variances of noise and blur, which, in turn, are used to obtain an image without discernible distortions. A set of statistical features computed from the image and its complex wavelet sub-bands are used as input to the ANN. In the proposed method, we solve the inverse Rayleigh function numerically for speckle reduction and use the Richardson-Lucy algorithm for de-blurring. The performance of this method is compared with that of the traditional methods by applying them to a synthetic, physical phantom and clinical data, which confirms better restoration results by the proposed method.

MAP-Based Motion Refinement Algorithm for Block-Based Motion-Compensated Frame Interpolation

A new motion vector field (MVF) refinement algorithm is proposed for block-based motion-compensated frame interpolation. Under the assumption that an observed MVF, such as the result of a block-based motion estimation (BME), is a degraded version of the true MVF, the true MVF is estimated from the observation through maximum a posteriori probability (MAP) estimation. To define the posterior probability of the true MVF, the degradation is modeled as a locally stationary additive Gaussian noise, so the variance of the noise represents the unreliability of the observed motion vector (MV). The noise variance is directly estimated from the observation vector and its select neighbors. The prior distribution of the true MVF is designed to rely on the distances between the MV and its neighbors and to properly smooth the false MVs in the observation. The MAP estimate of the true MVF is obtained via the iterative conditional mode method. The outcome is a set of iterative update equations, which produce the kth estimate of the true MV of a block by combining, according to the estimated noise variance, the observation and the neighboring (k - 1)th estimates. Experimental results prove that the proposed algorithm achieves performances comparable with those of several existing MAP-based BME algorithms at a much lower computational complexity.

Noise level estimation method with application to EMD-based signal denoising

This paper proposes a new signal noise level estimation approach by local regions. The estimated noise variance is applied as the threshold for an improved empirical mode decomposition (EMD) based signal denoising method. The proposed estimation method can effectively extract the candidate regions for the noise level estimation by measuring the correlation coefficient between noisy signal and a Gaussian filtered signal. For the improved EMD based method, the situation of decomposed intrinsic mode function (IMFs) which contains noise and signal simultaneously are taken into account. Experimental results from two simulated signals and an X-ray pulsar signal demonstrate that the proposed method can achieve better performance than the conventional EMD and wavelet transform (WT) based denoising methods.

SAR image de-noising based on texture strength and weighted nuclear norm minimization

As synthetic aperture radar (SAR) has been widely used nearly in every field, SAR image de-noising became a very important research field. A new SAR image de-noising method based on texture strength and weighted nuclear norm minimization (WNNM) is proposed. To implement blind de-noising, the accurate estimation of noise variance is very important. So far, it is still a challenge to estimate SAR image noise level accurately because of the rich texture. Principal component analysis (PCA) and the low rank patches selected by image texture strength are used to estimate the noise level. With the help of noise level, WNNM can be expected to SAR image de-noising. Experimental results show that the proposed method outperforms many excellent de-noising algorithms such as Bayes least squares-Gaussian scale mixtures (BLS-GSM) method, non-local means (NLM) filtering in terms of both quantitative measure and visual perception quality.

A novel intelligent strategy for probabilistic electricity price forecasting: Wavelet neural network based modified dolphin optimization algorithm

To simplify decision making of market participants, a careful and reliable electricity market price forecasting method is indispensable. Nevertheless, due to the Instability in market clearing prices (MCPs), it is rather tough to forecast MCPs accurately. Using probabilistic forecasting is a new so lution to overcome the low accuracy of forecast. Transformation from traditional point forecasts to probabilistic interval forecasts is too important to model the uncertainties of forecasts. Thus the decision making activities of market participants are supported against uncertainties and risks effectively. In this paper a hybrid approach to achieve prediction intervals (PIs) of MCPs is proposed that modified dolphin echolocation optimization algorithm (MDEOA) is applied to estimate point forecasts, model uncertainties, and noise variance. This proposed electricity price probabilistic forecasting method is evaluated by a generalized and comprehensive framework. To test the proposed hybrid method, real price data from Ontario, New England, and, Australian electricity markets are used and effectiveness of the method is validated.

SU‐F‐I‐07: CBCT Denoising Based On Adaptive Dictionary Learning Algorithms

Purpose:We proposed a new dictionary learning algorithm (AK‐SVD) based on K‐SVD. AK‐SVD can denoise the CBCT image, and did not need the noise information as prior knowledge.Methods:The AK‐SVD had two steps: signal sparse representation, and then dictionary optimization. The CBCT image was sparse, and there were limited big coefficients. The other coefficients were zero or near zero. In the sparse representation step of traditional K‐SVD, the noise variance was used as a threshold to select the big representation coefficients. This increased the complexity of the algorithm. The denoising result also was affected by the accuracy of the noise variance estimation, especially in non‐Gaussian noise. In AK‐SVD we used the average of the existing big coefficients as a threshold. The new found coefficient was compared with the threshold. If it was bigger than this threshold, it will be determined as the big coefficient, and be added to the set of existing big coefficients. The finding process continued. If it was smaller than this threshold, the finding process was end.This threshold was not related to the noise variance, and based on this method we improved the traditional K‐SVD.Results:In the synthetic experiments about designing dictionary from synthetic signals, the correct rate of dictionary learning by the AK‐SVD was similar with the ideal results of the K‐SVD where the noise variance was known. However, the AK‐SVD algorithm did not need to evaluate the noise variance, so it had lower computational complexity and wider adaptability. In the denoising experiment about the CBCT image corrupted by the non‐Gaussian noise, AK‐SVD has an advantage in terms of texture.Conclusion:The AK‐SVD can work well with the noise variance unknown, and it had lower computational complexity and wider adaptability than K‐SVD.This work was jointly supported by National Natural Science Foundation of China (61471226), Natural Science Foundation for Distinguished Young Scholars of Shandong Province (JQ201516), China Postdoctoral Science Foundation (2015T80739, 2014M551949), and research funding from Jinan (201401221).

Soft decision cooperative spectrum sensing with noise uncertainty reduction

Cognitive radio (CR) is a potential strategy for opportunistic access of idle resources to solve the conflicts between spectrum scarcity and underutilization. Spectrum sensing (SS) constitutes the most critical part in CR systems since the CR needs to detect the presence of primary signals reliably and quickly. Energy detection (ED) based SS is considered as the most preferable SS technique due to its simplicity and applicability. However, it is influenced by the effect of noise uncertainty which highly degrades its sensing performance. Cooperative spectrum sensing (CSS) is also introduced to mitigate some sensing problems such as multipath fading, shadowing, and hidden node problems. In this paper, we propose an enhanced fusion center (FC) rule for soft decision CSS using ED, which highly alleviates the noise uncertainty effect and enhances the sensing performance of cognitive radio networks (CRNs). In the proposed fusion rule, to increase the probability of detection and decrease the probability of false alarm, two dynamic thresholds are utilized by the FC. These thresholds are toggled based on predicting the current activity of the primary user (PU), and their values are dynamically changed based on estimating the noise uncertainty factor of the collected energy measurements from the CRs. To effectively predict (estimate) the current PU activity (the noise uncertainty factor), simple successive averaging processes over the collected energy measurements (the estimated noise variances) are performed by the FC, respectively. Theoretical analysis is performed on the proposed fusion rule for soft decision CSS to evaluate its enhanced false alarm and detection probabilities using different data combining schemes. Performance evaluations are also investigated to confirm the theoretical claims and to prove the effectiveness of the proposed scheme over the conventional ED based soft decision CSS.

Image Denoising Using Quadtree-Based Nonlocal Means With Locally Adaptive Principal Component Analysis

In this letter, we present an efficient image denoising method combining quadtree-based nonlocal means (NLM) and locally adaptive principal component analysis. It exploits nonlocal multiscale self-similarity better, by creating sub-patches of different sizes using quadtree decomposition on each patch. To achieve spatially uniform denoising, we propose a local noise variance estimator combined with denoiser based on locally adaptive principal component analysis. Experimental results demonstrate that our proposed method achieves very competitive denoising performance compared with state-of-the-art denoising methods, even obtaining better visual perception at high noise levels.

Robust adaptive filtering using recursive weighted least squares with combined scale and variable forgetting factors.

In this paper, a new adaptive robustified filter algorithm of recursive weighted least squares with combined scale and variable forgetting factors for time-varying parameters estimation in non-stationary and impulsive noise environments has been proposed. To reduce the effect of impulsive noise, whether this situation is stationary or not, the proposed adaptive robustified approach extends the concept of approximate maximum likelihood robust estimation, the so-called M robust estimation, to the estimation of both filter parameters and noise variance simultaneously. The application of variable forgetting factor, calculated adaptively with respect to the robustified prediction error criterion, provides the estimation of time-varying filter parameters under a stochastic environment with possible impulsive noise. The feasibility of the proposed approach is analysed in a system identification scenario using finite impulse response (FIR) filter applications.

Estimation of gravity noise variance and signal covariance parameters in least squares collocation with considering data resolution

<p>The article describes an implementation of the negative log-likelihood function in the determination of uncorrelated noise standard deviation together with the parameters of spherical signal covariance model in least squares collocation (LSC) of gravity anomalies. The correctness and effectiveness of restricted maximum likelihood (REML) estimates are fully validated by leave-one-out validation (LOO). These two complementary methods give an opportunity to inspect the parametrization of the signal and uncorrelated noise in details and can provide some guidance related to the estimation of individual parameters. The study provides the practical proof that noise variance is related with the data resolution, which is often neglected and the information on a priori noise variance is based on the measurement error. The data have been downloaded from U.S. terrestrial gravity database and resampled to enable an analysis with four different horizontal resolutions. These data are intentionally the same, as in the previous study of the same author, with the application of the planar covariance model. The aim is to compare the results from two different covariance models, which have different covariance approximation at larger distances. The most interesting outputs from this study confirm previous observations on the relations of the data resolution, a priori noise variance, signal spectrum and LSC accuracy.</p>

SDME Quality Measure based Stopping Criteria for Iterative Deblurring Algorithms

Deblurring from motion problem with or without noise is ill-posed inverse problem and almost all inverse problem require some sort of parameter selection. Quality of restored image in iterative motion deblurring is dependent on optimal stopping point or regularization parameter selection. At optimal point reconstructed image is best matched to original image and for other points either data mismatch occurs and over smoothing is resulted. The methods used for optimal parameter selection are formulated based on correct estimation of noise variance or with restrictive assumption on noise. Some methods involved heavy computation and produce delay in final output. In this paper we propose the method which calculate visual image quality of reconstructed image with the help of Second derivative like measure of enhancement (SDME) and helps to efficiently decide optimal stopping condition which has been checked for leading image deblurring algorithm. It do not require any estimation of noise variance or no heavy computation are needed. Simulation has been done for various images including standard images for different degradation and noise condition. For test leading deblurring algoritham of Blind and Semi-Blind deblurring of Natural Images using Alternate direction method of minimizer (ADMM) is considered. The obtained results for synthetically blurred images are good even under noisy condition with ? ISNR average values 0.2914 dB. The proposed whiteness measures seek powerful solution to iterative deblurring algorithms in deciding automatic stopping criteria.

Speckle Reduction Algorithm for Medical Ultrasound Imaging

Image denoising has remained a fundamental problem in the field of medical image processing. Ultrasound images are most commonly used in medical diagnostics. Unfortunately the quality of ultrasound imaging is degraded by the presence of signal dependent noise called speckle noise. It is necessary to apply an efficient despeckling technique to compensate for data corruption. Recently, wavelet and multi scale based methods, due to their excellent localisation property, have rapidly become very popular for image denoising. In this paper, a new noise variance estimation technique is proposed which attempts to map the median value of the pixelwise noise standard deviation. Then, an adaptive threshold is applied to shrink the noisy coefficients. The experimental results show that the proposed algorithm performs well for different ultrasound images and over a large range of noise variances.

Adaptive Two-stage Spectrum Sensing under Noise Uncertainty in Cognitive Radio Networks

To utilize licensed spectrum bands efficiently, spectrum sensing needs to be accurate and fast. The occurrence of noise uncertainty and the lower in received PU signal power due to the distance between the transmitter and the receiver, path loss, are the main challenges that has a great impact on the accuracy of spectrum sensing.
 In this paper, we propose a new scheme of two-stage spectrum sensing, “Adaptive Two-stage Spectrum Sensing (ATSS)”, under noise uncertainty environment. ATSS is a modified of a conventional two-stage spectrum sensing where the decision threshold of both stages are adapted on the distance, estimated noise variance and calculated noise uncertainty interval. Therefore, ATSS improves the detection performance of the existing spectrum sensing and is robust to noise uncertainty.
 The contribution of this paper is three-fold. First, an unreliable detection and wasted stage activation of a conventional two-stage spectrum sensing are reduced. Second, noise uncertainty is addressed. Third, a new parameter, critical distance ( ), is proposed in order to reduce computational burden and sensing time of the first stage.

Low-rank approach for image nonblind deconvolution with variance estimation

We develop a low-rank approach for image restoration by exploiting the image’s nonlocal self-similarity. We assume that the matrix stacked by the vectors of nonlocal similar patches is of low rank and has sparse singular values. Based on this assumption, we propose a new image deconvolution algorithm that decouples the deblurring and denoising steps. Specifically, in the deblurring step, we involve a regularized inversion of the blur in the Fourier domain, which amplifies and colors the noise and corrupts the image information. Hence, in the denoising step, a singular-value decomposition of similar packed patches is used to efficiently remove the colored noise. Furthermore, we derive an approach to update the estimation of noise variance for setting the threshold parameter at each iteration. Experimental results clearly show that the proposed algorithm outperforms many state-of-the-art deblurring algorithms such as iterative decoupled deblurring BM3D in terms of both improvement in signal-to-noise-ratio and visual perception quality.