Estimation Of Noise Parameters Research Articles

Noise Removal Based on Tensor Modelling for Hyperspectral Image Classification

With the current state-of-the-art computer aided manufacturing tools, the spatial resolution of hyperspectral sensors is becoming increasingly higher thus making it easy to obtain much more detailed information of the scene captured. However, the improvement of the spatial resolution also brings new challenging problems to address with signal dependent photon noise being one of them. Unlike the signal independent thermal noise, the variance of photon noise is dependent on the signal, therefore many denoising methods developed for the stationary noise cannot be applied directly to the photon noise. To make things worse, both photon and thermal noise coexist in the captured hyperspectral image (HSI), thus making it more difficult to whiten noise. In this paper, we propose a new denoising framework to cope with signal dependent nonwhite noise (SDNW), Pre-estimate—Whitening—Post-estimate (PWP) loop, to reduce both photon and thermal noise in HSI. Previously, we proposed a method based on multidimensional wavelet packet transform and multi-way Wiener filter which performs both white noise and spectral dimensionality reduction, referred to as MWPT-MWF, which was restricted to white noise. We get inspired from this MWPT-MWF to develop a new iterative method for reducing photon and thermal noise. Firstly, the hyperspectral noise parameters estimation (HYNPE) algorithm is used to estimate the noise parameters, the SD noise is converted to an additive white Gaussian noise by pre-whitening procedure and then the whitened HSI is denoised by the proposed method SDNW-MWPT-MWF. As comparative experiments, the Multiple Linear Regression (MLR) based denoising method and tensor-based Multiway Wiener Filter (MWF) are also used in the denoising framework. An HSI captured by Reflective Optics System Imaging Spectrometer (ROSIS) is used in the experiments and the denoising performances are assessed from various aspects: the noise whitening performance, the Signal-to-Noise Ratio (SNR), and the classification performance. The results on the real-world airborne hyperspectral image HYDICE (Hyperspectral Digital Imagery Collection Experiment) are also presented and analyzed. These experiments show that it is worth taking into account noise signal-dependency hypothesis for processing HYDICE and ROSIS HSIs.

Parameter Estimation of Signal-Dependent Random Noise in CMOS/CCD Image Sensor Based on Numerical Characteristic of Mixed Poisson Noise Samples.

Parameter estimation of Poisson-Gaussian signal-dependent random noise in the complementary metal-oxide semiconductor/charge-coupled device image sensor is a significant step in eliminating noise. The existing estimation algorithms, which are based on finding homogeneous regions, acquire the pair of the variances of noise and the intensities of every homogeneous region to fit the linear or piecewise linear curve and ascertain the noise parameters accordingly. In contrast to the existing algorithms, in this study, the Poisson noise samples of all homogeneous regions in every block image are pieced together to constitute a larger sample following the mixed Poisson noise distribution; then, the mean and variance of the mixed Poisson noise sample are deduced. Next, the mapping function among the noise parameters to be estimated—variance of Poisson-Gaussian noise and that of Gaussian noise corresponding to the stitched region in every block image—is constructed. Finally, the unbiased estimations of noise parameters are calculated from the mapping functions of all the image blocks. The experimental results confirm that the proposed method can obtain lower mean absolute error values of estimated noise parameters than the conventional ones.

Communication Signal Pre-Processing in Impulsive Noise: A Bandpass Myriad Filtering-Based Method

In impulsive noise modeled as symmetric $\alpha $ -stable ( ${\mathrm{S\alpha S}}$ ) distribution, it is known that signal processing techniques performed in bandpass can generally achieve better performance than in baseband. In this letter, we propose a bandpass myriad filtering-based pre-processing method for a communication receiver in ${\mathrm{S\alpha S}}$ noise. The adopted myriad filter is designed based on the estimated parameters of ${\mathrm{S\alpha S}}$ noise. The observation data vector, which is used to estimate the transmitted signal, is constructed by choosing specific data from the received bandpass signal, so that two critical requirements for myriad filter can be met. Furthermore, a new method is proposed to estimate the ${\mathrm{S\alpha S}}$ noise parameters, for which the influence of signal is alleviated by an elaborately designed finite impulse response filter. Comparing with the existing methods, numerical simulations validate the superior performance of our proposed bandpass myriad filtering with new noise parameter estimation.

An Adaptive Markov Random Field for Structured Compressive Sensing.

Exploiting intrinsic structures in sparse signals underpins the recent progress in compressive sensing (CS). The key for exploiting such structures is to achieve two desirable properties: generality (i.e., the ability to fit a wide range of signals with diverse structures) and adaptability (i.e., being adaptive to a specific signal). Most existing approaches, however, often only achieve one of these two properties. In this study, we propose a novel adaptive Markov random field sparsity prior for CS, which not only is able to capture a broad range of sparsity structures, but also can adapt to each sparse signal through refining the parameters of the sparsity prior with respect to the compressed measurements. To maximize the adaptability, we also propose a new sparse signal estimation where the sparse signals, support, noise and signal parameter estimation are unified into a variational optimization problem, which can be effectively solved with an alternative minimization scheme. Extensive experiments on three real-world datasets demonstrate the effectiveness of the proposed method in recovery accuracy, noise tolerance, and runtime.

Sparse Bayesian Learning with joint noise robustness and signal sparsity

This study concerns the issue of jointly enhancing noise robustness and promoting signal sparsity in Sparse Bayesian Learning (SBL), which aims at addressing the performance deficiency of sparse signal recovery due to uninformative data with low signal-to-noise ratios. In particular, the authors propose a hierarchical prior noise model with a signal-dependent parametrisation and incorporate it into developing the robust SBL algorithms for sparse signal recovery. The main contribution of the proposed approach is twofold. The first is the new consideration of noise-robustness enhancement in building SBL algorithms, which devotes to noise awareness in counteracting outliers in measurements. Specifically, the idea of signal-sparsity enforcing is extended to build a Least Absolute Deviation like loss criterion with the proposed hierarchical prior model of measurement noise. The second is the novelty of using the signal-dependent parametrisation in the proposed noise model. Indeed, the signal-dependent mechanism plays an indispensable role in producing the reliable noise parameter estimation jointly with updating signal model parameters under the fast SBL framework. In addition to numerical simulation studies, the real-life application of radio tomographic imaging is presented to validate the proposed approach.

Ultimate Precision of Adaptive Noise Estimation.

We consider the estimation of noise parameters in a quantum channel, assuming the most general strategy allowed by quantum mechanics. This is based on the exploitation of unlimited entanglement and arbitrary quantum operations, so that the channel inputs may be interactively updated. In this general scenario, we draw a novel connection between quantum metrology and teleportation. In fact, for any teleportation-covariant channel (e.g., Pauli, erasure, or Gaussian channel), we find that adaptive noise estimation cannot beat the standard quantum limit, with the quantum Fisher information being determined by the channel's Choi matrix. As an example, we establish the ultimate precision for estimating excess noise in a thermal-loss channel, which is crucial for quantum cryptography. Because our general methodology applies to any functional that is monotonic under trace-preserving maps, it can be applied to simplify other adaptive protocols, including those for quantum channel discrimination. Setting the ultimate limits for noise estimation and discrimination paves the way for exploring the boundaries of quantum sensing, imaging, and tomography.

Taming outliers in pulsar-timing datasets with hierarchical likelihoods and Hamiltonian sampling

Pulsar-timing datasets have been analyzed with great success using probabilistic treatments based on Gaussian distributions, with applications ranging from studies of neutron-star structure to tests of general relativity and searches for nanosecond gravitational waves. As for other applications of Gaussian distributions, outliers in timing measurements pose a significant challenge to statistical inference, since they can bias the estimation of timing and noise parameters, and affect reported parameter uncertainties. We describe and demonstrate a practical end-to-end approach to perform Bayesian inference of timing and noise parameters robustly in the presence of outliers, and to identify these probabilistically. The method is fully consistent (i.e., outlier-ness probabilities vary in tune with the posterior distributions of the timing and noise parameters), and it relies on the efficient sampling of the hierarchical form of the pulsar-timing likelihood. Such sampling has recently become possible with a "no-U-turn" Hamiltonian sampler coupled to a highly customized reparametrization of the likelihood; this code is described elsewhere, but it is already available online. We recommend our method as a standard step in the preparation of pulsar-timing-array datasets: even if statistical inference is not affected, follow-up studies of outlier candidates can reveal unseen problems in radio observations and timing measurements; furthermore, confidence in the results of gravitational-wave searches will only benefit from stringent statistical evidence that datasets are clean and outlier-free.

Bernoulli-Langevin Wind Speed Model for Simulation of Storm Events

Abstract We present a simple nonlinear dynamics Langevin model for predicting the instationary wind speed profile during storm events typically accompanying extreme low-pressure situations. It is based on a second-degree Bernoulli equation with δ-correlated Gaussian noise and may complement stationary stochastic wind models. Transition between increasing and decreasing wind speed and (quasi) stationary normal wind and storm states are induced by the sign change of the controlling time-dependent rate parameter k(t). This approach corresponds to the simplified nonlinear laser dynamics for the incoherent to coherent transition of light emission that can be understood by a phase transition analogy within equilibrium thermodynamics [H. Haken, Synergetics, 3rd ed., Springer, Berlin, Heidelberg, New York 1983/2004.]. Evidence for the nonlinear dynamics two-state approach is generated by fitting of two historical wind speed profiles (low-pressure situations “Xaver” and “Christian”, 2013) taken from Meteorological Terminal Air Report weather data, with a logistic approximation (i.e. constant rate coefficients k) to the solution of our dynamical model using a sum of sigmoid functions. The analytical solution of our dynamical two-state Bernoulli equation as obtained with a sinusoidal rate ansatz k(t) of period T (=storm duration) exhibits reasonable agreement with the logistic fit to the empirical data. Noise parameter estimates of speed fluctuations are derived from empirical fit residuals and by means of a stationary solution of the corresponding Fokker-Planck equation. Numerical simulations with the Bernoulli-Langevin equation demonstrate the potential for stochastic wind speed profile modeling and predictive filtering under extreme storm events that is suggested for applications in anticipative air traffic management.

An approach for estimating time-variable rates from geodetic time series

There has been considerable research in the literature focused on computing and forecasting sea-level changes in terms of constant trends or rates. The Antarctic ice sheet is one of the main contributors to sea-level change with highly uncertain rates of glacial thinning and accumulation. Geodetic observing systems such as the Gravity Recovery and Climate Experiment (GRACE) and the Global Positioning System (GPS) are routinely used to estimate these trends. In an effort to improve the accuracy and reliability of these trends, this study investigates a technique that allows the estimated rates, along with co-estimated seasonal components, to vary in time. For this, state space models are defined and then solved by a Kalman filter (KF). The reliable estimation of noise parameters is one of the main problems encountered when using a KF approach, which is solved by numerically optimizing likelihood. Since the optimization problem is non-convex, it is challenging to find an optimal solution. To address this issue, we limited the parameter search space using classical least-squares adjustment (LSA). In this context, we also tested the usage of inequality constraints by directly verifying whether they are supported by the data. The suggested technique for time-series analysis is expanded to classify and handle time-correlated observational noise within the state space framework. The performance of the method is demonstrated using GRACE and GPS data at the CAS1 station located in East Antarctica and compared to commonly used LSA. The results suggest that the outlined technique allows for more reliable trend estimates, as well as for more physically valuable interpretations, while validating independent observing systems.

Joint Signal Parameter Estimation in Non–Gaussian Noise by the Method of Polynomial Maximization

Abstract This paper considers the adaptation of the method of polynomial maximization for synthesis of the polynomial algorithms of joint signal parameter estimation in non-Gaussian noise. It is shown that the nonlinear processing of samples, the moment and the cumulant description of random variables in the form of cumulant coefficients of the third and higher orders can decrease the variance of joint parameters estimation as compared with the well-known results.

Noise reduction of speech signals using time-varying and multi-band adaptive gain control for smart digital hearing protectors

In this paper, a single-channel speech enhancement algorithm based on non-linear and multi-band Adaptive Gain Control (AGC) is proposed. The algorithm requires neither Signal-to-Noise Ratio (SNR) nor noise parameters estimation. It reduces the background noise in the temporal domain rather than the spectral domain using a non-linear and automatically adjustable gain function for multi-band AGC. The gain function varies in time and is deduced from the temporal envelope of each frequency band to highly compress the frequency regions where noise is present and lightly compress the frequency regions where speech is present. Objective evaluation using the PESQ (Perceptual Evaluation of Speech Quality) metric shows that the proposed algorithm performs better than three benchmarks, namely: the spectral subtraction, the Wiener filter based on a priori SNR estimation and a band-pass modulation filtering algorithm. In addition, blind subjective tests show that the proposed algorithm introduces less musical noise compared to the benchmark algorithms and was preferred 78.8% of the time in terms of signal quality. The proposed algorithm is implemented in a miniature low power digital signal processor to validate its feasibility and complexity for smart hearing protection in noisy environments.

THE NANOGRAV NINE-YEAR DATA SET: NOISE BUDGET FOR PULSAR ARRIVAL TIMES ON INTRADAY TIMESCALES

ABSTRACT The use of pulsars as astrophysical clocks for gravitational wave (GW) experiments demands the highest possible timing precision. Pulse times of arrival (TOAs) are limited by stochastic processes that occur in the pulsar itself, along the line of sight through the interstellar medium, and in the measurement process. On timescales of seconds to hours, the TOA variance exceeds that from template-fitting errors due to additive noise. We assess contributions to the total variance from two additional effects: amplitude and phase jitter intrinsic to single pulses and changes in the interstellar impulse response from scattering. The three effects have different dependencies on time, frequency, and pulse signal-to-noise ratio. We use data on 37 pulsars from the North American Nanohertz Observatory for GWs to assess the individual contributions to the overall intraday noise budget for each pulsar. We detect jitter in 22 pulsars and estimate the average value of rms jitter in our pulsars to be ∼ 1 % ?> of pulse phase. We examine how jitter evolves as a function of frequency and find evidence for evolution. Finally, we compare our measurements with previous noise parameter estimates and discuss methods to improve GW detection pipelines.

Self-adapting denoising, alignment and reconstruction in electron tomography in materials science

An automatic procedure for electron tomography is presented. This procedure is adapted for specimens that can be fashioned into a needle-shaped sample and has been evaluated on inorganic samples. It consists of self-adapting denoising, automatic and accurate alignment including detection and correction of tilt axis, and 3D reconstruction. We propose the exploitation of a large amount of information of an electron tomography acquisition to achieve robust and automatic mixed Poisson–Gaussian noise parameter estimation and denoising using undecimated wavelet transforms. The alignment is made by mixing three techniques, namely (i) cross-correlations between neighboring projections, (ii) common line algorithm to get a precise shift correction in the direction of the tilt axis and (iii) intermediate reconstructions to precisely determine the tilt axis and shift correction in the direction perpendicular to that axis. Mixing alignment techniques turns out to be very efficient and fast. Significant improvements are highlighted in both simulations and real data reconstructions of porous silicon in high angle annular dark field mode and agglomerated silver nanoparticles in incoherent bright field mode. 3D reconstructions obtained with minimal user-intervention present fewer artefacts and less noise, which permits easier and more reliable segmentation and quantitative analysis. After careful sample preparation and data acquisition, the denoising procedure, alignment and reconstruction can be achieved within an hour for a 3D volume of about a hundred million voxels, which is a step toward a more routine use of electron tomography.

ITERATIVE METHOD FOR BLIND EVALUATION OF MIXED NOISE CHARACTERISTICS ON IMAGES

A new method for blind estimation of mixed noise parameters is proposed. The method is based on line fitting into a set of cluster centers obtained from scatter-plot of local variance and mean estimates. Improved estimation of cluster centers is performed on basis of fourth-order statistical moment analysis. The estimation results for the proposed method are compared to the results for other known methods using images from TID2008 database. It is shown that the proposed method provides estimation accuracy comparable to the estimation accuracy of the method based on maximum likelihood estimation of image and noise characteristics (which is considered the best among the existing methods). An advantage of our method is that it is considerably faster.

An Image Denoising Method for Noises Based on Mixed Gaussian Distribution in HSV Color Space

Traditional image noise model is created for color images in RGB color space. Difiering with the traditional model, noise model is created in HSV space towards origins of noise generation in this paper. It is supposed that noise images based on mixed Gaussian distribution with zero mean value on three dimensions, including hue, saturation and value, are quite similar to actual situations. For images are characterized by simple background, EM algorithm is applied to estimation of noise parameters and related parameters are applied to wavelet threshold denoising in this paper. Results of the experiment show that both estimation and denoising are satisfactory.

A new noise covariance matrix estimation method of Kalman filter for satellite clock errors

The satellite clock plays a key role in the global navigation satellite system (GNSS). The accuracy of GNSS and its applications depend on the quality of the satellite clock. Therefore, precisely estimating and predicting the satellite clock is an important issue in the fields of GNSS and its application. As an optimal estimation algorithm, Kalman filter has been used to estimate and predict the satellite clock. However, in a conventional Kalman filter algorithm, the noise covariance matrices of satellite clock need to be predetermined, which restricts its further applications since the noise covariance matrices, especially the process noise covariance matrix, are usually unknown in the real cases. With inappropriate noise covariance matrices, the state estimation of conventional Kalman filter is suboptimal. To cope with this problem, a new noise covariance matrix estimation method of Kalman filter is proposed, and then we apply it to the problem of satellite clock estimation and prediction. Considering the fact that the process noise covariance matrix depends on the unknown noise parameters, the problem of estimating process noise covariance matrix can be solved by estimating the unknown noise parameters. First, the correlation between the Kalman innovations is used to establish a linear relationship with the unknown noise parameters. Then the unknown parameters can be estimated by least-squares estimation. Finally, the satellite clock can be estimated and predicted with the estimated noise parameters. In the new method, no prior information about the noise parameters is needed. Even with some extreme prior noise parameters, the new method can also work very well and has good convergence properties. For comparison, we conduct two experiments using the new method and the adaptively robust Kalman filter with classified adaptive factors based on opening windows separately, both results are consistent with each other very well, which verifies the correctness and effectiveness of this new method.

노이즈 매개변수 예측 기반 고속 노이즈 제거 방식

In this paper, a fast single image blind denoising algorithm is presented, where noise parameters are estimated by local statistics of an observed degraded image without a prior information about the additive noise. The estimated noise parameters are used to define the constraints on the noise detection which is coupled with the 1st-order Markov Random Field. In addition, an adaptive modified weighted Gaussian filter is introduced, where variable window sizes and weighting coefficients defined by the constraints are used to control the degree of the smoothness of the reconstructed image. The experimental results demonstrate the capability of the proposed algorithm. Please put the abstract of paper here.

Joint estimation of state and noise parameters in a linear dynamic system with impulsive measurement noise: Application to OFDM systems

Interference mitigation is one of the main challenges in wireless communication, especially in ad hoc networks. In such context, the Multiple Access Interference (MAI) is known to be of an impulsive nature. Therefore, the conventional Gaussian assumption is inadequate to model this type of interference. Nevertheless, it can be accurately modeled by stable distributions. In fact, it was shown in literature that the α-stable distribution is a useful tool to model impulsive data. In this paper, we tackle the problem of noise compensation in ad hoc networks. More precisely, this issue is addressed within an Orthogonal Frequency Division Multiplexing (OFDM) transmission link assuming a symmetric α-stable model for the signal distortion due to MAI. Based on Bayesian estimation, the proposed approach estimates the transmitted OFDM symbols in the time domain using the Sequential Monte Carlo (SMC) methods. Unlike existing schemes, we consider the more realistic case where the impulsive noise parameters are assumed to be unknown at the receiver. Consequently, our approach deals also with the difficult task of noise parameters estimation which can be very useful for other purposes such as target tracking in wireless sensor networks or channel estimation. Simulations results, provided in terms of Mean Square Error (MSE) and Bit Error Rate (BER), illustrate the efficiency and the robustness of this scheme.

Lossy compression of hyperspectral images based on noise parameters estimation and variance stabilizing transform

A problem of lossy compression of hyperspectral images is considered. A specific aspect is that we assume a signal-dependent model of noise for data acquired by new generation sensors. Moreover, a signal-dependent component of the noise is assumed dominant compared to a signal-independent noise component. Sub-band (component-wise) lossy compression is studied first, and it is demonstrated that optimal operation point (OOP) can exist. For such OOP, the mean square error between compressed and noise-free images attains global or, at least, local minimum, i.e., a good effect of noise removal (filtering) is reached. In practice, we show how compression in the neighborhood of OOP can be carried out, when a noise-free image is not available. Two approaches for reaching this goal are studied. First, lossy compression directly applied to the original data is considered. According to another approach, lossy compression is applied to images after direct variance stabilizing transform (VST) with properly adjusted parameters. Inverse VST has to be performed only after data decompression. It is shown that the second approach has certain advantages. One of them is that the quantization step for a coder can be set the same for all sub-band images. This offers favorable prerequisites for applying three-dimensional (3-D) methods of lossy compression for sub-band images combined into groups after VST. Two approaches to 3-D compression, based on the discrete cosine transform, are proposed and studied. A first approach presumes obtaining the reference and “difference” images for each group. A second performs compression directly for sub-images in a group. We show that it is a good choice to have 16 sub-images in each group. The abovementioned approaches are tested for Hyperion hyperspectral data. It is demonstrated that the compression ratio of about 15–20 can be provided for hyperspectral image compression in the neighborhood of OOP for 3-D coders, which is sufficiently larger than for component-wise compression and lossless coding.

Image Sensor Noise Parameter Estimation by Variance Stabilization and Normality Assessment.

High-quality image denoising requires taking into account the dependence of the noise distribution on the original image. The parameters of this dependence are often unknown and we propose a new method to estimate them here. Using an optimization procedure, we find a variance-stabilizing transformation, which transforms the input image into an image with signal-independent noise. Principal component analysis of blocks of the transformed image allows estimation of the variance of the signal-independent noise so that the parameters of the original noise model can be computed. The image blocks for processing are selected in such a way that they have low stochastic texture strength but preserve the noise distribution. The algorithm does not require the original image to have homogeneous areas and can accurately process images with regular textures. It has high computational efficiency and smaller maximum estimation error compared with the state of the art. Our experiments have also shown that denoising with the noise parameters estimated by this method leads to the same results as denoising with the true noise parameters.