Estimation Of Noise Parameters Research Articles

HYPERSPECTRAL IMAGE MIXED NOISE REDUCTION BASED ON IMPROVED K-SVD ALGORITHM

We propose an algorithm for mixed noise reduction in Hyperspectral Imagery (HSI). The hyperspectral data cube is considered as a three order tensor. These tensors give a clear view about both spatial and spectral modes. The HSI provides ample spectral information to identify and distinguish spectrally unique materials, thus they are spectrally over determined. Tensor representation is three ordered thus can simultaneously deal with the two spatial dimensions and one spectral dimension of HSI to achieve a satisfying noise reduction performance. The image analysis application like Classification, unmixing, subpixel mapping and target detection are performed in a very accurate manner due to the development of hyperspectral remote sensing technology as it provides large amount of spatial and spectral information. This entire denoising process is based on the K-SVD denoising algorithm. This method of denoising can efficiently remove a variety of mixed or single noise by applying sparse regularization of small image patches. It also maintains the image texture in a clear manner. The learned dictionary used clearly helps in removing the noise. Our work involved in minimizing model to remove mixed noise such as Impulse noise, Gaussian-Gaussian mixture and Gaussian-Impulse noise from the HSI data. The weighted rank-one approximation problem is solved using a new iterative scheme and the low rank approximation can be obtained by singular value decomposition(SVD).A new weighting data fidelity function which is much easier to optimize is used which has the same minimizer as the original likelihood function. The weighting function in the model can be determined by the algorithm itself, and it plays a role of noise detection in terms of the different estimated noise parameters.

Super-Resolution Reconstruction of Radar Tomographic Image Based on Image Decomposition

In this letter, the relationship between target scattering function and point spread function of radar tomographic imaging is discussed, and an inherent super-resolution reconstruction algorithm based on image decomposition (ID) is proposed. By removing the cross disturbance due to the resolution limitation, the exact radar images can be obtained. Furthermore, the total least-square regulation is applied to the ID-based algorithm in cases of additive white Gaussian noise and small parameter estimation error. Finally, the effectiveness of the proposed algorithm is demonstrated via numerical simulations.

On required accuracy of mixed noise parameter estimation for image enhancement via denoising

Abstract Characteristics of noise (type, statistics, spatial correlation) are nowadays exploited in many image denoising and enhancement methods. However, these characteristics are often unknown, and they have to be extracted from an image at hand. There are many powerful and accurate blind methods for noise variance estimation for the cases of additive and multiplicative noise models. However, more complicated noise models containing a mixture of signal-independent (SI) and signal-dependent (SD) components are often more adequate in practice. Parameters of both components have to be automatically estimated to be used in image enhancement. This paper addresses a question of required accuracy of such estimation. Analysis is carried out for color images processed by a filter based on discrete cosine transform. The influence of errors in mixed noise parameters estimation is studied in terms of filtering efficiency. This efficiency is characterized by the conventional criterion peak signal-to-noise ratio (PSNR) and two visual quality metrics, PSNR human visual system masking (PSNR-HVS-M) and multi-scale structural similarity (MSSIM). If a reduction of filtering efficiency exceeds 0.5 dB (in terms of PSNR and PSNR-HVS-M) or 0.005 (in terms of MSSIM), mixed noise parameters estimation is assumed to be unacceptable. As the result, it is shown that SI and SD noise parameters have to be estimated with a relative error not exceeding 20%…30%.

A New Recursive Identification Method for Weighted Criterion

In time-series system modeling traditional criterions only consider current estimation error while the past and global prediction errors are usually overlooked. By integrating both the estimation error and the difference between neighbor prediction errors, a novel weighted identification criterion was presented. Based on this criterion the alternations of the two-step algorithm is constructed through separating the system parameters estimation and noise parameters estimation for the system disturbed by colored noise, which could result in oscillation and instability. An extended one-step recursive algorithm for the weighted identification criterion is introduced in this paper. For the input-output system disturbed by colored noise, the prediction gradients and the gradient of the pseudo linear regression vector are given. The gradient iterative algorithm and the direct adaptive method (DAM), the new one-step recursive algorithm are proposed by a series of estimation process optimizations. Finally, a simulation example is conducted to demonstrate the efficiency of this new method.

SAR Image Denoising Using an Improved Adaptive Bitateral Filter

Synthetic aperture radar (SAR) images are inherently affected by multiplicative speckle noise. The presence of speckle damages radiometric resolution, at the same time, it hampers the human interpretation and scene analysis for SAR images. On the base of studying and analyzing the mathematical model of the bilateral filter, the paper proposed a modified adaptive bilateral filter (MABF). First, it separates non-independent two-dimensional Gaussian filter into two independent one-dimensional Gaussian filter, which improves the operation speed greatly. Then through the effective noise parameter estimation, it adaptively selects optimal parameters, which improves the filtering effect. The real SAR image data is used to test the presented method and the experimental results verify that MABF is feasible and effective.

Simplified noise model parameter estimation for signal-dependent noise

In this paper, we present a noise parameter estimation method using a simplified signal-dependent noise model. The generic Poisson–Gaussian noise model is simplified to a Gaussian–Gaussian noise model. From the simplified noise model, we experimentally verify that the value obtained by the robust median estimator is almost the same as the mean of the noise standard deviation. Based on this property, the noise model parameters are estimated by the least square method. Simulation results show that the estimation performance using our proposed algorithm is compatible with the performance of the existing method. Our method can generate good parameter estimation results with reduced computational complexity.

Online estimation of noise parameters for Kalman filter

A Bayesian probabilistic method is proposed for online estimation of the process noise and measurement noise parameters for Kalman filter. Kalman filter is a well-known recursive algorithm for state estimation of dynamical systems. In this algorithm, it is required to prescribe the covariance matrices of the process noise and measurement noise. However, inappropriate choice of these covariance matrices substantially deteriorates the performance of the Kalman filter. In this paper, a probabilistic method is proposed for online estimation of the noise parameters which govern the noise covariance matrices. The proposed Bayesian method not only estimates the optimal noise parameters but also quantifies the associated estimation uncertainty in an online manner. By utilizing the estimated noise parameters, reliable state estimation can be accomplished. Moreover, the proposed method does not assume any stationarity condition of the process noise and/or measurement noise. By removing the stationarity constraint, the proposed method enhances the applicability of the state estimation algorithm for nonstationary circumstances generally encountered in practice. To illustrate the efficacy and efficiency of the proposed method, examples using a fifty-story building with different stationarity scenarios of the process noise and measurement noise are presented.

Statistical texture retrieval in noise using complex wavelets

This paper investigates the use of complex wavelets for statistical texture retrieval in a noisy environment, in which the query image is contaminated by noise. To account for the presence of noise, the feature extraction step is based on parameter estimation in noise where features are extracted from the noisy query image by modeling the magnitude and phase of complex subband coefficients of the clean image, and relating the model's parameters to the noisy coefficients. In addition to using only the magnitude or phase which is in the form of the relative phase, we incorporate both magnitude and phase information to further improve the accuracy rate. The simulation results show the retrieval rate improvement by estimating the clean parameters from the noisy query image instead of assuming that the query image is clean. Furthermore, using both magnitude and phase of complex coefficients improves the accuracy rate from using either magnitude or phase alone, and that using complex-valued wavelets yields higher rate than using real-valued wavelets.

Sub-Optimum Receiver Architecture for AWGN Channel with Symmetric Alpha-Stable Interference

In many scenarios, the undesirable disturbance at a communication receiver has to be modeled as the sum of Gaussian noise and impulsive interference for which closed form probability density function (pdf) generally does not exist. This makes optimum receiver implementation difficult. In this paper, motivated by the heavy tail nature of the resultant pdf, an alternate parametric solution is proposed. After estimation of the appropriate parameters, the alternate solution may then be written in closed form, leading to a relatively simple architecture. Simulation results show that the proposed receiver performance, in terms of bit error rate (BER), is almost indistinguishable from the optimum receiver while outperforming other sub-optimum receivers. Noise parameter estimation using empirical characteristic functions is also discussed.

Multidimensional prewhitening for enhanced signal reconstruction and parameter estimation in colored noise with Kronecker correlation structure

Parameter estimation of multidimensional data in the presence of colored noise or interference with a Kronecker product covariance structure, which appears in electroencephalogram/magnetoencephalogram and multiple-input multiple-output applications, is addressed. In order to improve the accuracy of the multidimensional subspace-based estimation techniques designed for white noise, prewhitening algorithms are devised by exploiting the Kronecker structure of the noise covariance matrix. We first contribute to the development of the multidimensional prewhitening (MD-PWT) scheme which assumes that noise-only measurements are available. By applying prewhitening sequentially along various dimensions using the corresponding correlation factors estimated from the noise-only measurements, the MD-PWT significantly improves the performance of the closed-form parallel factor decomposition based parameter estimator (CFP-PE) with a small number of noise-only snapshots. When noise-only measurements are unavailable, an iterative joint estimation of noise and signal parameters and prewhitening algorithm is proposed by iteratively applying the MD-PWT and CFP-PE. Adaptive convergence thresholds are designed as the stopping conditions such that the optimal number of iterations is automatically determined. Simulation results show that the iterative scheme performs nearly the same as the MD-PWT with noise statistics, in all scenarios except for a special one of intermediate signal-to-noise ratios and high noise correlation levels.

Image informative maps for component-wise estimating parameters of signal-dependent noise

We deal with the problem of blind parameter estimation of signal-dependent noise from mono-component image data. Multispectral or color images can be processed in a component-wise manner. The main results obtained rest on the assumption that the image texture and noise parameters estimation problems are interdependent. A two-dimensional fractal Brownian motion (fBm) model is used for locally describing image texture. A polynomial model is assumed for the purpose of describing the signal-dependent noise variance dependence on image intensity. Using the maximum likelihood approach, estimates of both fBm-model and noise parameters are obtained. It is demonstrated that Fisher information (FI) on noise parameters contained in an image is distributed nonuniformly over intensity coordinates (an image intensity range). It is also shown how to find the most informative intensities and the corresponding image areas for a given noisy image. The proposed estimator benefits from these detected areas to improve the estimation accuracy of signal-dependent noise parameters. Finally, the potential estimation accuracy (Cramer-Rao Lower Bound, or CRLB) of noise parameters is derived, providing confidence intervals of these estimates for a given image. In the experiment, the proposed and existing state-of-the-art noise variance estimators are compared for a large image database using CRLB-based statistical efficiency criteria.

Using the Wireless and PLC Channels for Diversity

Performance of indoor home networks can be improved by simultaneous use of wireless and powerline communication (PLC) channels. A narrowband model representing an OFDM subcarrier is used to analyze the performance of several diversity combining schemes including optimum combining (OC), saturated metric combining (SMC) and maximal ratio combining (MRC). Results from BER analysis show that SMC achieves good performance in highly impulsive noise and is relatively insensitive to error in noise parameter estimates. Indoor measurements from 3 detached homes show that parallel wireless and PLC channels have a wide, but similar, signal-to-noise ratio (SNR) range. Measurement data is used with link throughput analysis to show that wireless/PLC diversity can be used to minimize the likelihood of low throughput links.

A Weighted Dictionary Learning Model for Denoising Images Corrupted by Mixed Noise

This paper proposes a general weighted l(2)-l(0) norms energy minimization model to remove mixed noise such as Gaussian-Gaussian mixture, impulse noise, and Gaussian-impulse noise from the images. The approach is built upon maximum likelihood estimation framework and sparse representations over a trained dictionary. Rather than optimizing the likelihood functional derived from a mixture distribution, we present a new weighting data fidelity function, which has the same minimizer as the original likelihood functional but is much easier to optimize. The weighting function in the model can be determined by the algorithm itself, and it plays a role of noise detection in terms of the different estimated noise parameters. By incorporating the sparse regularization of small image patches, the proposed method can efficiently remove a variety of mixed or single noise while preserving the image textures well. In addition, a modified K-SVD algorithm is designed to address the weighted rank-one approximation. The experimental results demonstrate its better performance compared with some existing methods.

Nonlinear Compensation Using the Gauss–Newton Method for Noise-Robust Speech Recognition

In this paper, we present the Gauss-Newton method as a unified approach to estimating noise parameters of the prevalent nonlinear compensation models, such as vector Taylor series (VTS), data-driven parallel model combination (DPMC), and unscented transform (UT), for noise-robust speech recognition. While iterative estimation of noise means in a generalized EM framework has been widely known, we demonstrate that such approaches are variants of the Gauss-Newton method. Furthermore, we propose a novel noise variance estimation algorithm that is consistent with the Gauss-Newton principle. The formulation of the Gauss-Newton method reduces the noise estimation problem to determining the Jacobians of the corrupted speech parameters. For sampling-based compensations, we present two methods, sample Jacobian average (SJA) and cross-covariance (XCOV), to evaluate these Jacobians. The proposed noise estimation algorithm is evaluated for various compensation models on two tasks. The first is to fit a Gaussian mixture model (GMM) model to artificially corrupted samples, and the second is to perform speech recognition on the Aurora 2 database. The significant performance improvements confirm the efficacy of the Gauss-Newton method to estimating the noise parameters of the nonlinear compensation models.

Demosaicking of Noisy Bayer-Sampled Color Images With Least-Squares Luma-Chroma Demultiplexing and Noise Level Estimation

This paper adapts the least-squares luma-chroma demultiplexing (LSLCD) demosaicking method to noisy Bayer color filter array (CFA) images. A model is presented for the noise in white-balanced gamma-corrected CFA images. A method to estimate the noise level in each of the red, green, and blue color channels is then developed. Based on the estimated noise parameters, one of a finite set of configurations adapted to a particular level of noise is selected to demosaic the noisy data. The noise-adaptive demosaicking scheme is called LSLCD with noise estimation (LSLCD-NE). Experimental results demonstrate state-of-the-art performance over a wide range of noise levels, with low computational complexity. Many results with several algorithms, noise levels, and images are presented on our companion web site along with software to allow reproduction of our results.

On Some Applications of Poisson Point Processes

Poisson point processes play important role in various domains of Probability Theory and Mathematical Statistics. In this article, we investigate only two applications of Poisson point processes: a generated white noise problem and parameters estimation problem. This work continues the investigations started in paper Egorov and Kondybaev (2009).

Radial Basic Networks M-training by Asymmetric Influence Functions

We consider robust approach to radial basic networks training under the presence of measurement noise, which have asymmetric distributions. For minimization of the suggested asymmetric functionals the algorithms of Gauss−Newton and Levenberg−Marquardt are used. Estimation of noise parameters is done by the algorithm of stochastic approximation. Results of modeling, which confirm efficiency of the suggested approach, are stated.

Iterative integral parameter identification of a respiratory mechanics model.

BackgroundPatient-specific respiratory mechanics models can support the evaluation of optimal lung protective ventilator settings during ventilation therapy. Clinical application requires that the individual’s model parameter values must be identified with information available at the bedside. Multiple linear regression or gradient-based parameter identification methods are highly sensitive to noise and initial parameter estimates. Thus, they are difficult to apply at the bedside to support therapeutic decisions.MethodsAn iterative integral parameter identification method is applied to a second order respiratory mechanics model. The method is compared to the commonly used regression methods and error-mapping approaches using simulated and clinical data. The clinical potential of the method was evaluated on data from 13 Acute Respiratory Distress Syndrome (ARDS) patients.ResultsThe iterative integral method converged to error minima 350 times faster than the Simplex Search Method using simulation data sets and 50 times faster using clinical data sets. Established regression methods reported erroneous results due to sensitivity to noise. In contrast, the iterative integral method was effective independent of initial parameter estimations, and converged successfully in each case tested.ConclusionThese investigations reveal that the iterative integral method is beneficial with respect to computing time, operator independence and robustness, and thus applicable at the bedside for this clinical application.

Quantitative analysis of LISA pathfinder test-mass noise

In this paper we discuss two main problems associated with the analysis of the data from LISA Pathfinder (LPF): i) Excess noise detection and ii) Noise parameter identification. The mission is focused on the low frequency region ([0.1; 10] mHz) of the available signal spectrum. In such a region the signal is dominated by the force noise acting on test masses. Noise analysis is expected to deal with a limited amount of non-Gaussian data, since the spectrum statistics will be far from Gaussian and the lowest available frequency is limited by the data length. In this paper we analyze the details of the expected statistics for spectral data and develop two suitable excess noise estimators. One is based on the statistical properties of the integrated spectrum, the other is based on Kolmogorov-Smirnov test. The sensitivity of the estimators is discussed theoretically for independent data, then the algorithms are tested on LPF synthetic data. The test on realistic LPF data allows the effect of spectral data correlations on the efficiency of the different noise excess estimators to be highlighted. It also reveals the versatility of the Kolmogorov-Smirnov approach, which can be adapted to provide reasonable results on correlated data from a modified version of the standard equations for the inversion of the test statistic. Closely related to excess noise detection, the problem of noise parameter identification in non-Gaussian data is approached in two ways. One procedure is based on maximum likelihood estimator and another is based on the Kolmogorov-Smirnov goodness of fit estimator. Both approaches provide unbiased and accurate results for noise parameter estimation and demonstrate superior performance with respect to standard weighted least-squares and Huber's norm.

Signal-Dependent Noise Modeling and Model Parameter Estimation in Hyperspectral Images

In this paper, a novel method to characterize random noise sources in hyperspectral (HS) images is proposed. Noise is described using a parametric model that accounts for the dependence of noise variance on the useful signal. Such model takes into account the photon noise contribution and is therefore suitable for noise characterization in the data acquired by new-generation HS sensors where electronic noise is not dominant. A new algorithm is developed for the estimation of noise parameters which consists of two steps. First, the noise and signal realizations are extracted from the original image by resorting to the multiple-linear-regression-based approach. Then, the model parameters are estimated by using a maximum likelihood approach. The new method does not require the intervention of a human operator and the selection of homogeneous regions in the scene. The performance of the new technique is analyzed on simulated HS data. Results on real data are also presented and discussed. Images acquired with a new-generation HS camera are analyzed to give an experimental evidence of the dependence of random noise on the signal level and to show the results of the estimation algorithm. The algorithm is also applied to a well-known Airborne Visible/Infrared Imaging Spectrometer data set in order to show its effectiveness when noise is dominated by the signal-independent term.