Showing papers on "White noise published in 2013"

Image Noise Level Estimation by Principal Component Analysis

Abstract: The problem of blind noise level estimation arises in many image processing applications, such as denoising, compression, and segmentation. In this paper, we propose a new noise level estimation method on the basis of principal component analysis of image blocks. We show that the noise variance can be estimated as the smallest eigenvalue of the image block covariance matrix. Compared with 13 existing methods, the proposed approach shows a good compromise between speed and accuracy. It is at least 15 times faster than methods with similar accuracy, and it is at least two times more accurate than other methods. Our method does not assume the existence of homogeneous areas in the input image and, hence, can successfully process images containing only textures.

Time Series Analysis Using Composite Multiscale Entropy

Abstract: Multiscale entropy (MSE) was recently developed to evaluate the complexity of time series over different time scales. Although the MSE algorithm has been successfully applied in a number of different fields, it encounters a problem in that the statistical reliability of the sample entropy (SampEn) of a coarse-grained series is reduced as a time scale factor is increased. Therefore, in this paper, the concept of a composite multiscale entropy (CMSE) is introduced to overcome this difficulty. Simulation results on both white noise and 1/f noise show that the CMSE provides higher entropy reliablity than the MSE approach for large time scale factors. On real data analysis, both the MSE and CMSE are applied to extract features from fault bearing vibration signals. Experimental results demonstrate that the proposed CMSE-based feature extractor provides higher separability than the MSE-based feature extractor.

Signals embedded in the radial velocity noise - Periodic variations in the τ Ceti velocities

Abstract: Context. The abilities of radial velocity exoplanet surveys to detect the lowest-mass extra-solar planets are currently limited by a combination of instrument precision, lack of data, and 'jitter'. Jitter is a general term for any unknown features in the noise, and reflects a lack of detailed knowledge of stellar physics (asteroseismology, starspots, magnetic cycles, granulation, and other stellar surface phenomena), as well as the possible underestimation of instrument noise. Aims. We study an extensive set of radial velocities for the star HD 10700 (τ Ceti) to determine the properties of the jitter arising from stellar surface inhomogeneities, activity, and telescope-instrument systems, and perform a comprehensive search for planetary signals in the radial velocities. Methods. We performed Bayesian comparisons of statistical models describing the radial velocity data to quantify the number of significant signals and the magnitude and properties of the excess noise in the data. We reached our goal by adding artificial signals to the 'flat' radial velocity data of HD 10700 and by seeing which one of our statistical noise models receives the greatest posterior probabilities while still being able to extract the artificial signals correctly from the data. We utilised various noise components to assess properties of the noise in the data and analyse the HARPS, AAPS, and HIRES data for HD 10700 to quantify these properties and search for previously unknown low-amplitude Keplerian signals. Results. According to our analyses, moving average components with an exponential decay with a timescale from a few hours to few days, and Gaussian white noise explains the jitter the best for all three data sets. Fitting the corresponding noise parameters results in significant improvements of the statistical models and enables the detection of very weak signals with amplitudes below 1 m s-1 level in our numerical experiments. We detect significant periodicities that have no activity-induced counterparts in the combined radial velocities. Three of these signals can be seen in the HARPS data alone, and a further two can be inferred by utilising the AAPS and Keck data. These periodicities could be interpreted as corresponding to planets on dynamically stable close-circular orbits with periods of 13.9, 35.4, 94, 168, and 640 days and minimum masses of 2.0, 3.1, 3.6, 4.3, and 6.6 M⊕, respectively.

Additive White Gaussian Noise Level Estimation in SVD Domain for Images

Abstract: Accurate estimation of Gaussian noise level is of fundamental interest in a wide variety of vision and image processing applications as it is critical to the processing techniques that follow. In this paper, a new effective noise level estimation method is proposed on the basis of the study of singular values of noise-corrupted images. Two novel aspects of this paper address the major challenges in noise estimation: 1) the use of the tail of singular values for noise estimation to alleviate the influence of the signal on the data basis for the noise estimation process and 2) the addition of known noise to estimate the content-dependent parameter, so that the proposed scheme is adaptive to visual signals, thereby enabling a wider application scope of the proposed scheme. The analysis and experiment results demonstrate that the proposed algorithm can reliably infer noise levels and show robust behavior over a wide range of visual content and noise conditions, and that is outperforms relevant existing methods.

A Modeling-Free Inversion-Based Iterative Feedforward Control for Precision Output Tracking of Linear Time-Invariant Systems

Abstract: In this paper, we propose a modeling-free inversion-based iterative feedforward control (MIIFC) approach for high-speed output tracking of single-input single-output linear time-invariant systems The recently developed inversion-based iterative learning control (IIC) techniques provide a straightforward manner to quantify and account for the effect of dynamics uncertainty on iterative learning control performance, thereby arriving at rapid convergence of the iterative control input However, dynamics model and thereby the modeling process are still needed, and the model quality directly limits the performance of the IIC techniques The main contribution of this paper is the development of the MIIFC algorithm to eliminate the dynamics modeling process, and significantly improve the tracking performance The disturbance (measurement noise) effect on the tracking precision is addressed in the convergence analysis of the MIIFC algorithm The allowable disturbance/noise level to guarantee the convergence is quantified in frequency domain, and the noise level can be estimated through the noise spectrum measured before the whole operation The MIIFC technique is demonstrated by applying it to the output tracking of a piezotube scanner on an atomic force microscope The experimental results showed that precision output tracking of a frequency-rich desired trajectory with power spectrum similar to a band-limited white noise can be achieved

Electroelastic modeling and experimental validations of piezoelectric energy harvesting from broadband random vibrations of cantilevered bimorphs

Abstract: We present electroelastic modeling, analytical and numerical solutions, and experimental validations of piezoelectric energy harvesting from broadband random vibrations. The modeling approach employed herein is based on a distributed-parameter electroelastic formulation to ensure that the effects of higher vibration modes are included, since broadband random vibrations, such as Gaussian white noise, might excite higher vibration modes. The goal is to predict the expected value of the power output and the mean-square shunted vibration response in terms of the given power spectral density (PSD) or time history of the random vibrational input. The analytical method is based on the PSD of random base excitation and distributed-parameter frequency response functions of the coupled voltage output and shunted vibration response. The first of the two numerical solution methods employs the Fourier series representation of the base acceleration history in an ordinary differential equation solver while the second method uses an Euler‐Maruyama scheme to directly solve the resulting electroelastic stochastic differential equations. The analytical and numerical simulations are compared with several experiments for a brass-reinforced PZT-5H bimorph under different random excitation levels. The simulations exhibit very good agreement with the experimental measurements for a range of resistive electrical boundary conditions and input PSD levels. It is also shown that lightly damped higher vibration modes can alter the expected power curve under broadband random excitation. Therefore, the distributed-parameter modeling and solutions presented herein can be used as a more accurate alternative to the existing single-degree-of-freedom solutions for broadband random vibration energy harvesting.

Well-Posedness And Accuracy Of The Ensemble Kalman Filter In Discrete And Continuous Time

Abstract: The ensemble Kalman filter (EnKF) is a method for combining a dynamical model with data in a sequential fashion Despite its widespread use, there has been little analysis of its theoretical properties Many of the algorithmic innovations associated with the filter, which are required to make a useable algorithm in practice, are derived in an ad hoc fashion The aim of this paper is to initiate the development of a systematic analysis of the EnKF, in particular to do so in the small ensemble size limit The perspective is to view the method as a state estimator, and not as an algorithm which approximates the true filtering distribution The perturbed observation version of the algorithm is studied, without and with variance inflation Without variance inflation well-posedness of the filter is established; with variance inflation accuracy of the filter, with resepct to the true signal underlying the data, is established The algorithm is considered in discrete time, and also for a continuous time limit arising when observations are frequent and subject to large noise The underlying dynamical model, and assumptions about it, is sufficiently general to include the Lorenz '63 and '96 models, together with the incompressible Navier-Stokes equation on a two-dimensional torus The analysis is limited to the case of complete observation of the signal with additive white noise Numerical results are presented for the Navier-Stokes equation on a two-dimensional torus for both complete and partial observations of the signal with additive white noise

Memory Limited, Streaming PCA

Abstract: We consider streaming, one-pass principal component analysis (PCA), in the high-dimensional regime, with limited memory. Here, p-dimensional samples are presented sequentially, and the goal is to produce the k-dimensional subspace that best approximates these points. Standard algorithms require O(p2) memory; meanwhile no algorithm can do better than O(kp) memory, since this is what the output itself requires. Memory (or storage) complexity is most meaningful when understood in the context of computational and sample complexity. Sample complexity for high-dimensional PCA is typically studied in the setting of the spiked covariance model, where p-dimensional points are generated from a population covariance equal to the identity (white noise) plus a low-dimensional perturbation (the spike) which is the signal to be recovered. It is now well-understood that the spike can be recovered when the number of samples, n, scales proportionally with the dimension, p. Yet, all algorithms that provably achieve this, have memory complexity O(p2). Meanwhile, algorithms with memory-complexity O(kp) do not have provable bounds on sample complexity comparable to p. We present an algorithm that achieves both: it uses O(kp) memory (meaning storage of any kind) and is able to compute the k-dimensional spike with O(p log p) sample-complexity - the first algorithm of its kind. While our theoretical analysis focuses on the spiked covariance model, our simulations show that our algorithm is successful on much more general models for the data.

Constellation Optimization in the Presence of Strong Phase Noise

Abstract: In this paper, we address the problem of optimizing signal constellations for strong phase noise. The problem is investigated by considering three optimization formulations, which provide an analytical framework for constellation design. In the first formulation, we seek to design constellations that minimize the symbol error probability (SEP) for an approximate ML detector in the presence of phase noise. In the second formulation, we optimize constellations in terms of mutual information (MI) for the effective discrete channel consisting of phase noise, additive white Gaussian noise, and the approximate ML detector. To this end, we derive the MI of this discrete channel. Finally, we optimize constellations in terms of the MI for the phase noise channel. We give two analytical characterizations of the MI of this channel, which are shown to be accurate for a wide range of signal-to-noise ratios and phase noise variances. For each formulation, we present a detailed analysis of the optimal constellations and their performance in the presence of strong phase noise. We show that the optimal constellations significantly outperform conventional constellations and those proposed in the literature in terms of SEP, error floors, and MI.

Rough Burgers-like equations with multiplicative noise

Abstract: We construct solutions to vector valued Burgers type equations perturbed by a multiplicative space–time white noise in one space dimension. Due to the roughness of the driving noise, solutions are not regular enough to be amenable to classical methods. We use the theory of controlled rough paths to give a meaning to the spatial integrals involved in the definition of a weak solution. Subject to the choice of the correct reference rough path, we prove unique solvability for the equation and we show that our solutions are stable under smooth approximations of the driving noise.

Exploring a New Class of Non-stationary Spatial Gaussian Random Fields with Varying Local Anisotropy

Abstract: Gaussian random fields (GRFs) constitute an important part of spatial modelling, but can be computationally infeasible for general covariance structures. An efficient approach is to specify GRFs via stochastic partial differential equations (SPDEs) and derive Gaussian Markov random field (GMRF) approximations of the solutions. We consider the construction of a class of non-stationary GRFs with varying local anisotropy, where the local anisotropy is introduced by allowing the coefficients in the SPDE to vary with position. This is done by using a form of diffusion equation driven by Gaussian white noise with a spatially varying diffusion matrix. This allows for the introduction of parameters that control the GRF by parametrizing the diffusion matrix. These parameters and the GRF may be considered to be part of a hierarchical model and the parameters estimated in a Bayesian framework. The results show that the use of an SPDE with non-constant coefficients is a promising way of creating non-stationary spatial GMRFs that allow for physical interpretability of the parameters, although there are several remaining challenges that would need to be solved before these models can be put to general practical use.

Fundamental limitations of polynomial chaos for uncertainty quantification in systems with intermittent instabilities

Abstract: Here, we examine the suitability of truncated Polynomial Chaos Expansions (PCE) and truncated GramCharlier Expansions (GrChE) as possible methods for uncertainty quantification (UQ) in nonlinear systems with intermittency and positive Lyapunov exponents. These two methods rely on truncated Galerkin projections of either the system variables in a fixed polynomial basis spanning the ‘uncertain’ subspace (PCE) or a suitable eigenfunction expansion of the joint probability distribution associated with the uncertain evolution of the system (GrChE). Based on a simple, statistically exactly solvable non-linear and non-Gaussian test model, we show in detail that methods exploiting truncated spectral expansions, be it PCE or GrChE, have significant limitations for uncertainty quantification in systems with intermittent instabilities or parametric uncertainties in the damping. Intermittency and fat-tailed probability densities are hallmark features of the inertial and dissipation ranges of turbulence and we show that in such important dynamical regimes PCE performs, at best, similarly to the vastly simpler Gaussian moment closure technique utilized earlier by the authors in a different context for UQ within a framework of Empirical Information Theory. Moreover, we show that the non-realizability of the GrChE approximations is linked to the onset of intermittency in the dynamics and it is frequently accompanied by an erroneous blow-up of the second-order statistics at short times. These limitations of the two types of truncated spectral expansions arise from the following: (i) Non-uniform convergence in time of PCE and GrChE resulting in a rapidly increasing number of terms necessary for a good approximation of the random process as time evolves, (ii) Fundamental problems with capturing the constant flux of randomness due to white Gaussian noise forcing via finite truncations of the spectral representation of the associated Wiener process, (iii) Slow decay of PCE and GrChE coefficients in the presence of intermittency, hampering implementation of sparse truncation methods which have been widely used in nearly elliptic problems or in low Reynolds number flows. Rigorous justification of these limitations is richly illustrated by straightforward tests exploiting a simple nonlinear and non-Gaussian but statistically exactly solvable test model which is proposed here as a challenging benchmark for algorithms for UQ in systems with intermittency.

Fast noise variance estimation by principal component analysis

Abstract: Noise variance estimation is required in many image denoising, compression, and segmentation applications. In this work, we propose a fast noise variance estimation algorithm based on principal component analysis of image blocks. First, we rearrange image blocks into vectors and compute the covariance matrix of these vectors. Then, we use Bartlett's test in order to select the covariance matrix eigenvalues, which correspond only to noise. This allows estimating the noise variance as the average of these eigenvalues. Since the maximum possible number of eigenvalues corresponding to noise is utilized, it is enough to process only a small number of image blocks, which allows reduction of the execution time. The blocks to process are selected from image regions with the smallest variance. During our experiments involving seven state of the art methods, the proposed approach was signi_cantly faster than the methods with similar or higher accuracy. Meanwhile, the relative error of our estimator was always less than 15%. We also show that the proposed method can process images without homogeneous areas.

Characterization of an Optimized Off-Diagonal GMI-Based Magnetometer

Abstract: An optimized giant magneto-impedance effect magnetometer has been developed, based on an overall analysis of the measurement chain, including physical material properties, associated detection coil parameters, and equivalent magnetic noise performances. The field response model for the sensing element and the noise model yield good agreement with experimental results. The noise performance of the magnetometer, approximately 1.7 pT/√{Hz} in the white noise region, with a band-pass of about 70 kHz, is competitive with that of other technologies. Present limitations are clearly established, leaving room for further improvements.

White noise-induced spiral waves and multiple spatial coherence resonances in a neuronal network with type I excitability ☆

Abstract: White noise-induced pattern formation is studied in a network composed of Morris–Lecar neuronal models with type I excitability and with initial values higher than that of the resting potential. The appearance and disappearance of spiral waves, as well as the transitions between spiral wave patterns with different kinds of complexity characterized by the normalized spatial autocorrelation function, enable changes in the order of the network so as to exhibit a scenario with two or more locally maximal peaks, as can be clearly seen in the signal to noise ratio curves, as the noise intensity is adjusted from small to large in a wide range. A possible physical mechanism of the multiple resonances based on the dynamics of type I excitability and initial values is provided. The potential biological significance of the noise-induced spiral waves is discussed.

SNR Estimation for Multi-dimensional Cognitive Receiver under Correlated Channel/Noise

Abstract: In addition to Spectrum Sensing (SS) capability required by a Cognitive Radio (CR), Signal to Noise Ratio (SNR) estimation of the primary signals at the CR receiver is crucial in order to adapt its coverage area dynamically using underlay techniques. In practical scenarios, channel and noise may be correlated due to various reasons and SNR estimation techniques with the assumption of white noise and uncorrelated channel may not be suitable for estimating the primary SNR. In this paper, firstly, we study the performance of different eigenvalue-based SS techniques in the presence of channel or/and noise correlation. Secondly, we carry out detailed theoretical analysis of the signal plus noise hypothesis to derive the asymptotic eigenvalue probability distribution function (a.e.p.d.f.) of the received signal's covariance matrix under the following two cases: (i) correlated channel and white noise, and (ii) correlated channel and correlated noise, which is the main contribution of this paper. Finally, an SNR estimation technique based on the derived a.e.p.d.f is proposed in the presence of channel/noise correlation and its performance is evaluated in terms of normalized Mean Square Error (MSE). It is shown that the PU SNR can be reliably estimated when the CR sensing module is aware of the channel/noise correlation.

Probability-dependent gain-scheduled control for discrete stochastic delayed systems with randomly occurring nonlinearities

Abstract: SUMMARY In this paper, the gain-scheduled control problem is addressed by using probability-dependent Lyapunov functions for a class of discrete-time stochastic delayed systems with randomly occurring sector nonlinearities. The sector nonlinearities are assumed to occur according to a time-varying Bernoulli distribution with measurable probability in real time. The multiplicative noises are given by means of a scalar Gaussian white noise sequence with known variances. The aim of the addressed gain-scheduled control problem is to design a controller with scheduled gains such that, for the admissible randomly occurring nonlinearities, time delays and external noise disturbances, the closed-loop system is exponentially mean-square stable. Note that the designed gain-scheduled controller is based on the measured time-varying probability and is therefore less conservative than the conventional controller with constant gains. It is shown that the time-varying controller gains can be derived in terms of the measurable probability by solving a convex optimization problem via the semi-definite programme method. A simulation example is exploited to illustrate the effectiveness of the proposed design procedures. Copyright © 2012 John Wiley & Sons, Ltd.

Errors and their mitigation at the kirchhoff-law-johnson-noise secure key exchange.

Abstract: A method to quantify the error probability at the Kirchhoff-law-Johnson-noise (KLJN) secure key exchange is introduced. The types of errors due to statistical inaccuracies in noise voltage measurements are classified and the error probability is calculated. The most interesting finding is that the error probability decays exponentially with the duration of the time window of single bit exchange. The results indicate that it is feasible to have so small error probabilities of the exchanged bits that error correction algorithms are not required. The results are demonstrated with practical considerations.

Long-time behaviour of a perturbed SIR model by white noise

Abstract: In this paper, we consider a stochastic SIR model with perturbed disease transmission coefficient. We present sufficient conditions for the disease to extinct exponentially. In the case of persistence, we analyze long-time behaviour of densities of the distributions of the solution. We will prove that the densities of the solution can converge in $L^1$ to an invariant density under appropriate conditions. Also we find the support of the invariant density. Specially, when the intensity of white noise is relatively small, we find a new threshold for an epidemic to occur.

Bayesian Optimal Adaptive Estimation Using a Sieve Prior

Abstract: We derive rates of contraction of posterior distributions on non-parametric models resulting from sieve priors. The aim of the study was to provide general conditions to get posterior rates when the parameter space has a general structure, and rate adaptation when the parameter is, for example, a Sobolev class. The conditions employed, although standard in the literature, are combined in a different way. The results are applied to density, regression, nonlinear autoregression and Gaussian white noise models. In the latter we have also considered a loss function which is different from the usual l2 norm, namely the pointwise loss. In this case it is possible to prove that the adaptive Bayesian approach for the l2 loss is strongly suboptimal and we provide a lower bound on the rate.

Response probability density functions of Duffing-Van der Pol vibro-impact system under correlated Gaussian white noise excitations

Abstract: This paper aims to investigate the stationary probability density functions (PDFs) of a Duffing–Van der Pol vibro-impact system excited by correlated Gaussian white noise. With the help of non-smooth transformation, the stationary PDFs are formulated analytically by the stochastic averaging of energy envelope. The analytical results are verified by numerical simulation results. Stochastic bifurcations for different parameters are considered, and several special PDF forms are observed in this paper. The first form is the shape of the PDF of total energy can be similar to a crater, which has a minimum and a maximum. The second one is the shape of the joint PDF with three peaks, that is to say, the section of joint PDF has three maximum and two minimum. In addition, the influence of the degree of the correlation of Gaussian white noises is explored.

Asymptotic equivalence for nonparametric regression with non-regular errors

Abstract: Asymptotic equivalence in Le Cam’s sense for nonparametric regression experiments is extended to the case of non-regular error densities, which have jump discontinuities at their endpoints. We prove asymptotic equivalence of such regression models and the observation of two independent Poisson point processes which contain the target curve as the support boundary of its intensity function. The intensity of the point processes is of order of the sample size n and involves the jump sizes as well as the design density. The statistical model significantly differs from regression problems with Gaussian or regular errors, which are known to be asymptotically equivalent to Gaussian white noise models.

Pseudo-Linear Analysis of Bang-Bang Controlled Timing Circuits

Abstract: This paper describes an accurate, yet analytical method to predict the key characteristics of a bang-bang controlled timing loop: namely, the jitter transfer (JTRAN), jitter generation (JG), and jitter tolerance (JTOL). The analysis basically derives a linearized model of the system, where the bang-bang phase detector is modeled as a set of two linearized gain elements and an additive white noise source. This phase detector (PD) model is by far the most extensive one in literature, which can correctly estimate the effects of random jitter, transition density, and finite loop latency on the loop characteristics. The described pseudo-linear analysis assumes the presence of random jitter at the PD input and the minimum jitter necessary to keep the linear model valid is derived, based on a describing function analysis and Nyquist stability analysis. The presented analysis re-confirms the findings of prior theories and provides theoretical basis to the prior empirically-drawn equations, such as those for the quantization noise power and the gain reduction in presence of a finite loop delay. The predictions based on the presented analysis match well with the results from time-accurate behavioral simulations.