Showing papers on "White noise published in 2015"

Paracontrolled distributions and singular PDEs

Abstract: We introduce an approach to study certain singular partial differential equations (PDEs) which is based on techniques from paradifferential calculus and on ideas from the theory of controlled rough paths. We illustrate its applicability on some model problems such as differential equations driven by fractional Brownian motion, a fractional Burgers-type stochastic PDE (SPDE) driven by space-time white noise, and a nonlinear version of the parabolic Anderson model with a white noise potential.

An Efficient Statistical Method for Image Noise Level Estimation

Abstract: In this paper, we address the problem of estimating noise level from a single image contaminated by additive zero-mean Gaussian noise. We first provide rigorous analysis on the statistical relationship between the noise variance and the eigenvalues of the covariance matrix of patches within an image, which shows that many state-of-the-art noise estimation methods underestimate the noise level of an image. To this end, we derive a new nonparametric algorithm for efficient noise level estimation based on the observation that patches decomposed from a clean image often lie around a low-dimensional subspace. The performance of our method has been guaranteed both theoretically and empirically. Specifically, our method outperforms existing state-of-the-art algorithms on estimating noise level with the least executing time in our experiments. We further demonstrate that the denoising algorithm BM3D algorithm achieves optimal performance using noise variance estimated by our algorithm.

A Wong-Zakai theorem for stochastic PDEs

Abstract: We prove a version of the Wong-Zakai theorem for one-dimensional parabolic nonlinear stochastic PDEs driven by space-time white noise. As a corollary, we obtain a detailed local description of solutions.

Microseismic and seismic denoising via ensemble empirical mode decomposition and adaptive thresholding

Abstract: Random and coherent noise exists in microseismic and seismic data, and suppressing noise is a crucial step in seismic processing. We have developed a novel seismic denoising method, based on ensemble empirical mode decomposition (EEMD) combined with adaptive thresholding. A signal was decomposed into individual components called intrinsic mode functions (IMFs). Each decomposed signal was then compared with those IMFs resulting from a white-noise realization to determine if the original signal contained structural features or white noise only. A thresholding scheme then removed all nonstructured portions. Our scheme is very flexible, and it is applicable in a variety of domains or in a diverse set of data. For instance, it can serve as an alternative for random noise removal by band-pass filtering in the time domain or spatial prediction filtering in the frequency-offset domain to enhance the lateral coherence of seismic sections. We have determined its potential for microseismic and reflection seismic denoising by comparing its performance on synthetic and field data using a variety of methods including band-pass filtering, basis pursuit denoising, frequency-offset deconvolution, and frequency-offset empirical mode decomposition.

A Bernstein–von Mises theorem for smooth functionals in semiparametric models

Abstract: A Bernstein–von Mises theorem is derived for general semiparametric functionals. The result is applied to a variety of semiparametric problems in i.i.d. and non-i.i.d. situations. In particular, new tools are developed to handle semiparametric bias, in particular for nonlinear functionals and in cases where regularity is possibly low. Examples include the squared $L^{2}$-norm in Gaussian white noise, nonlinear functionals in density estimation, as well as functionals in autoregressive models. For density estimation, a systematic study of BvM results for two important classes of priors is provided, namely random histograms and Gaussian process priors.

Weak convergence for a spatial approximation of the nonlinear stochastic heat equation

Abstract: We find the weak rate of convergence of approximate solutions of the nonlinear stochastic heat equation, when discretized in space by a standard finite element method. Both multiplicative and additive noise is considered under different assumptions. This extends an earlier result of Debussche in which time discretization is considered for the stochastic heat equation perturbed by white noise. It is known that this equation only has a solution in one space dimension. In order to get results for higher dimensions, colored noise is considered here, besides the white noise case where considerably weaker assumptions on the noise term is needed. Integration by parts in the Malliavin sense is used in the proof. The rate of weak convergence is, as expected, essentially twice the rate of strong convergence.

Stepping molecular motor amid Lévy white noise

Abstract: We consider a model of a stepping molecular motor consisting of two connected heads. Directional motion of the stepper takes place along a one-dimensional track. Each head is subject to a periodic potential without spatial reflection symmetry. When the potential for one head is switched on, it is switched off for the other head. Additionally, the system is subject to the influence of symmetric, white Levy noise that mimics the action of external random forcing. The stepper exhibits motion with a preferred direction which is examined by analyzing the median of the displacement of a midpoint between the positions of the two heads. We study the modified dynamics of the stepper by numerical simulations. We find flux reversals as noise parameters are changed. Speed and direction appear to very sensitively depend on characteristics of the noise.

GPR Signal Denoising and Target Extraction With the CEEMD Method

Abstract: In this letter, we apply a time and frequency analysis method based on the complete ensemble empirical mode decomposition (CEEMD) method in ground-penetrating radar (GPR) signal processing. It decomposes the GPR signal into a sum of oscillatory components, with guaranteed positive and smoothly varying instantaneous frequencies. The key idea of this method relies on averaging the modes obtained by empirical mode decomposition (EMD) applied to several realizations of Gaussian white noise added to the original signal. It can solve the mode-mixing problem in the EMD method and improve the resolution of ensemble EMD (EEMD) when the signal has a low signal-to-noise ratio. First, we analyze the difference between the basic theory of EMD, EEMD, and CEEMD. Then, we compare the time and frequency analysis with Hilbert–Huang transform to test the results of different methods. The synthetic and real GPR data demonstrate that CEEMD promises higher spectral–spatial resolution than the other two EMD methods in GPR signal denoising and target extraction. Its decomposition is complete, with a numerically negligible error.

Wavelet Transform With Histogram-Based Threshold Estimation for Online Partial Discharge Signal Denoising

Abstract: Online condition assessment of the power system devices and apparatus is considered vital for robust operation, where partial discharge (PD) detection is employed as a diagnosis tool. PD measurements, however, are corrupted with different types of noises such as white noise, random noise, and discrete spectral interferences. Hence, the denoising of such corrupted PD signals remains a challenging problem in PD signal detection and classification. The challenge lies in removing these noises from the online PD signal measurements effectively, while retaining its discriminant features and characteristics. In this paper, wavelet-based denoising with a new histogram-based threshold function and selection rule is proposed. The proposed threshold estimation technique obtains two different threshold values for each wavelet sub-band and uses a prodigious thresholding function that conserves the original signal energy. Moreover, two signal-to-noise ratio (SNR) estimation techniques are derived to fit with actual PD signals corrupted with real noise. The proposed technique is applied on different acoustic and current measured PD signals to examine its performance under different noisy environments. The simulation results confirm the merits of the proposed denoising technique compared with other existing wavelet-based techniques by measuring four evaluation metrics: 1) SNR; 2) cross-correlation coefficient; 3) mean square error; and 4) reduction in noise level.

Optimal transport over a linear dynamical system

Abstract: We consider the problem of steering an initial probability density for the state vector of a linear system to a final one, in finite time, using minimum energy control. In the case where the dynamics correspond to an integrator ($\dot x(t) = u(t)$) this amounts to a Monge-Kantorovich Optimal Mass Transport (OMT) problem. In general, we show that the problem can again be reduced to solving an OMT problem and that it has a unique solution. In parallel, we study the optimal steering of the state-density of a linear stochastic system with white noise disturbance; this is known to correspond to a Schrodinger bridge. As the white noise intensity tends to zero, the flow of densities converges to that of the deterministic dynamics and can serve as a way to compute the solution of its deterministic counterpart. The solution can be expressed in closed-form for Gaussian initial and final state densities in both cases.

No Time for Dead Time: Timing analysis of bright black hole binaries with NuSTAR

Abstract: Timing of high-count rate sources with the NuSTAR Small Explorer Mission requires specialized analysis techniques. NuSTAR was primarily designed for spectroscopic observations of sources with relatively low count-rates rather than for timing analysis of bright objects. The instrumental dead time per event is relatively long (∼2.5 msec), and varies by a few percent event-to-event. The most obvious effect is a distortion of the white noise level in the power density spectrum (PDS) that cannot be modeled easily with the standard techniques due to the variable nature of the dead time. In this paper, we show that it is possible to exploit the presence of two completely independent focal planes and use the cross power density spectrum to obtain a good proxy of the white noise-subtracted PDS. Thereafter, one can use a Monte Carlo approach to estimate the remaining effects of dead time, namely a frequency-dependent modulation of the variance and a frequency-independent drop of the sensitivity to variability. In this way, most of the standard timing analysis can be performed, albeit with a sacrifice in signal to noise relative to what would be achieved using more standard techniques. We apply this technique to NuSTAR observations of the black hole binaries GX339−4, CygX-1 and GRS 1915+105.

Estimating the anomalous diffusion exponent for single particle tracking data with measurement errors - An alternative approach

Abstract: Accurately characterizing the anomalous diffusion of a tracer particle has become a central issue in biophysics. However, measurement errors raise difficulty in the characterization of single trajectories, which is usually performed through the time-averaged mean square displacement (TAMSD). In this paper, we study a fractionally integrated moving average (FIMA) process as an appropriate model for anomalous diffusion data with measurement errors. We compare FIMA and traditional TAMSD estimators for the anomalous diffusion exponent. The ability of the FIMA framework to characterize dynamics in a wide range of anomalous exponents and noise levels through the simulation of a toy model (fractional Brownian motion disturbed by Gaussian white noise) is discussed. Comparison to the TAMSD technique, shows that FIMA estimation is superior in many scenarios. This is expected to enable new measurement regimes for single particle tracking (SPT) experiments even in the presence of high measurement errors.

Cumulants-based modulation classification technique in multipath fading channels

Abstract: Automatic modulation classification (AMC) is a classical topic in the signal classification field and is often performed when the modulation type is adaptive. For typical modulation types such as M-PSK and M-QAM, the fourth-order cumulant statistics are usually used for modulation classification. Besides, it is also known that the AMC performance can be seriously degraded by the effects of multipath fading in wireless channels when compared with the ideal white Gaussian noise channel. In this study, a new modulation classification method is proposed, exploring different features of normalised fourth-order cumulant statistics for a modified blind channel estimation method in the multipath fading channel. The relationship between the cumulants of the received signal and the multipath fading effects is established to cope with the channel impulse response in the new algorithm. Simulation results show that the performance of the proposed AMC method is much improved than that of previously proposed ones in terms of the probability of correct classification.

Batch nonlinear continuous-time trajectory estimation as exactly sparse Gaussian process regression

Abstract: In this paper, we revisit batch state estimation through the lens of Gaussian process (GP) regression. We consider continuous-discrete estimation problems wherein a trajectory is viewed as a one-dimensional GP, with time as the independent variable. Our continuous-time prior can be defined by any nonlinear, time-varying stochastic differential equation driven by white noise; this allows the possibility of smoothing our trajectory estimates using a variety of vehicle dynamics models (e.g. `constant-velocity'). We show that this class of prior results in an inverse kernel matrix (i.e., covariance matrix between all pairs of measurement times) that is exactly sparse (block-tridiagonal) and that this can be exploited to carry out GP regression (and interpolation) very efficiently. When the prior is based on a linear, time-varying stochastic differential equation and the measurement model is also linear, this GP approach is equivalent to classical, discrete-time smoothing (at the measurement times); when a nonlinearity is present, we iterate over the whole trajectory to maximize accuracy. We test the approach experimentally on a simultaneous trajectory estimation and mapping problem using a mobile robot dataset.

Optimal Estimation for Discrete-Time Linear Systems in the Presence of Multiplicative and Time-Correlated Additive Measurement Noises

Abstract: In this paper, the state estimation problem for discrete-time linear systems influenced by multiplicative and time-correlated additive measurement noises is considered where the multiplicative noises are zero-mean white noise sequences, and the time-correlated additive noise is described by a linear system model with white noise An optimal linear estimator for the system under consideration is proposed, which does not require computing the inverse of state transition matrix The proposed estimator has a recursive structure, and has time-independent computation and storage load Computer simulations are carried out to demonstrate the performance of the proposed estimator The simulation results show the superiority of the proposed estimator

Simulations for single-dish intensity mapping experiments

Abstract: H I intensity mapping is an emerging tool to probe dark energy. Observations of the redshifted H I signal will be contaminated by instrumental noise, atmospheric and Galactic foregrounds. The latter is expected to be four orders of magnitude brighter than the H I emission we wish to detect. We present a simulation of single-dish observations including an instrumental noise model with 1/f and white noise, and sky emission with a diffuse Galactic foreground and H I emission. We consider two foreground cleaning methods: spectral parametric fitting and principal component analysis. For a smooth frequency spectrum of the foreground and instrumental effects, we find that the parametric fitting method provides residuals that are still contaminated by foreground and 1/f noise, but the principal component analysis can remove this contamination down to the thermal noise level. This method is robust for a range of different models of foreground and noise, and so constitutes a promising way to recover the H I signal from the data. However, it induces a leakage of the cosmological signal into the subtracted foreground of around 5 per cent. The efficiency of the component separation methods depends heavily on the smoothness of the frequency spectrum of the foreground and the 1/f noise. We find that as long as the spectral variations over the band are slow compared to the channel width, the foreground cleaning method still works.

Network-based estimation of time-dependent noise in GPS position time series

Abstract: Some estimates of GPS velocity uncertainties are very low, $$<$$ 0.1 mm/year with 10 years of data. Yet, residual velocities relative to rigid plate models in nominally stable plate interiors can be an order of magnitude larger. This discrepancy could be caused by underestimating low-frequency time-dependent noise in position time series, such as random walk. We show that traditional estimators, based on individual time series, are insensitive to low-amplitude random walk, yet such noise significantly increases GPS velocity uncertainties. Here, we develop a method for determining representative noise parameters in GPS position time series, by analyzing an entire network simultaneously, which we refer to as the network noise estimator (NNE). We analyze data from the aseismic central-eastern USA, assuming that residual motions relative to North America, corrected for glacial isostatic adjustment (GIA), represent noise. The position time series are decomposed into signal (plate rotation and GIA) and noise components. NNE simultaneously processes multiple stations with a Kalman filter and solves for average noise components for the network by maximum likelihood estimation. Synthetic tests show that NNE correctly estimates even low-level random walk, thus providing better estimates of velocity uncertainties than conventional, single station methods. To test NNE on actual data, we analyze a heterogeneous 15 station GPS network from the central-eastern USA, assuming the noise is a sum of random walk, flicker and white noise. For the horizontal time series, NNE finds higher average random walk than the standard individual station-based method, leading to velocity uncertainties a factor of 2 higher than traditional methods.

Compressive sensing based robust multispectral double-image encryption

Abstract: We demonstrate a multispectral double-image-based cryptosystem that exploits only a tiny number of random white noise samples for proper decryption Primarily, one of the two downsampled images is converted into the phase function after being shuffled by Arnold transform (AT), while the other image is modulated as an amplitude-based image after AT Consecutively, a full double-image encryption can be achieved by employing classical double random phase encryption (DRPE) technique in the fractional Fourier transform domain with corresponding fractional orders In this study, the encrypted complex data is randomly sampled via compressive sensing (CS) framework by which only 25% of the sparse white noise samples are being reserved to realize decryption with zero or small errors As a consequence, together with correct phase keys, fractional orders and proper inverse AT operators, lpminimization must be utilized to decrypt the original information Thus, in addition to the perfect image reconstruction, the proposed cryptosystem provides an additional layer of security to the conventional DRPE system Both the mathematical and numerical simulations were carried out to verify the feasibility as well as the robustness of the proposed system The simulation results are presented in order to demonstrate the effectiveness of the proposed system To the best of our knowledge, this is the first report on integrating CS with encrypted complex samples for information security

Co-localization of audio sources in images using binaural features and locally-linear regression

Abstract: This paper addresses the problem of localizing audio sources using binaural measurements. We propose a supervised formulation that simultaneously localizes multiple sources at different locations. The approach is intrinsically efficient because, contrary to prior work, it relies neither on source separation, nor on monaural segregation. The method starts with a training stage that establishes a locally linear Gaussian regression model between the directional coordinates of all the sources and the auditory features extracted from binaural measurements. While fixed-length wide-spectrum sounds (white noise) are used for training to reliably estimate the model parameters, we show that the testing (localization) can be extended to variable-length sparse-spectrum sounds (such as speech), thus enabling a wide range of realistic applications. Indeed, we demonstrate that the method can be used for audio-visual fusion, namely to map speech signals onto images and hence to spatially align the audio and visual modalities, thus enabling to discriminate between speaking and non-speaking faces. We release a novel corpus of real-room recordings that allow quantitative evaluation of the co-localization method in the presence of one or two sound sources. Experiments demonstrate increased accuracy and speed relative to several state-of-the-art methods.

In-Plane and Out-of-Plane MEMS Gyroscopes Based on Piezoresistive NEMS Detection

Abstract: This paper presents a new design and a complete characterization of amplitude-modulation gyroscopes based on piezoresistive nanogauges. The working principle and optimization criteria of in-plane and out-of-plane devices relying on double frame decoupling and levered sense mode are discussed in light of sensitivity and resolution theoretical predictions. The architecture of driving and sensing electronics is also presented. The reduced thermo-mechanical damping with respect to capacitive configurations, and the inherently high output signal leads to white noise performance in the mdps/ $\surd $ Hz range within an area smaller than 0.35 mm $^{\mathrm { {2}}}$ , at pressures in the millibar range. Sub-5-ppm linearity errors within 1000 dps are also demonstrated. [2015-0064]

Graph Theory-Based Approach for Stability Analysis of Stochastic Coupled Systems With Lévy Noise on Networks

Abstract: In this paper, a novel class of stochastic coupled systems with Levy noise on networks (SCSLNNs) is presented. Both white noise and Levy noise are considered in the networks. By exploiting graph theory and Lyapunov stability theory, criteria ensuring $p$ th moment exponential stability and stability in probability of these SCSLNNs are established, respectively. These principles are closely related to the topology of the network and the perturbation intensity of white noise and Levy noise. Moreover, to verify the theoretical results, stochastic coupled oscillators with Levy noise on a network and stochastic Volterra predator–prey system with Levy noise are performed. Finally, a numerical example about oscillators’ network is provided to illustrate the feasibility of our analytical results.

Estimation of the Noise Level Function Based on a Nonparametric Detection of Homogeneous Image Regions

Abstract: We propose a two-step algorithm that automatically estimates the noise level function of stationary noise from a single image, i.e., the noise variance as a function of the image intensity. First, the image is divided into small square regions and a non-parametric test is applied to decide weather each region is homogeneous or not. Based on Kendall's τ coefficient (a rank-based measure of correlation), this detector has a non-detection rate independent on the unknown distribution of the noise, provided that it is at least spatially uncorrelated. Moreover, we prove on a toy example, that its overall detection error vanishes with respect to the region size as soon as the signal to noise ratio level is non-zero. Once homogeneous regions are detected, the noise level function is estimated as a second order polynomial minimizing the l 1 error on the statistics of these regions. Numerical experiments show the efficiency of the proposed approach in estimating the noise level function, with a relative error under 10% obtained on a large data set. We illustrate the interest of the approach for an image denoising application.

Further results on dissipativity analysis of neural networks with time-varying delay and randomly occurring uncertainties

Abstract: In this paper, the problem of robust dissipativity is investigated for neural networks with both time-varying delay and randomly occurring uncertainties. The randomly occurring uncertainties are assumed to obey mutually uncorrelated Bernoulli-distributed white noise sequences. By constructing a new Lyapunov–Krasovskii functional, some improved delay-dependent dissipativity conditions are derived based on two integral inequalities, which are formulated in terms of linear matrix inequality. Furthermore, some information of activation function ignored in previous works has been taken into account in the resulting condition. The effectiveness and the improvement of the proposed approach are demonstrated by two illustrating numerical examples.

Modal Analysis Using Digital Image Correlation Technique: An Application to Artificial Wing Mimicking Beetle’s Hind Wing

Abstract: Understanding the dynamic behavior of structures has become increasingly important in the design process of any mechanical system. Therefore, the demands for improved structural performance have motivated the search for an effective method of structural dynamics testing, since the conventional methods are limited to the location of relatively few applied sensors. Due to the state-of-the-art optical technologies, the shape and deformation of a vibrating structure have been measured using 3-dimensional digital image correlation (DIC) technique. Although DIC has been used widely to construct the mode shape of the structure in modal measurement, it has rarely been applied to determine the full modal parameters (natural frequencies, mode shapes, damping factors). Therefore, this study presents an effective method to measure the full modal parameters of an artificial wing that mimics a beetle’s hind wing using the DIC technique. In our measurement, the artificial wing was mounted on a shaker, which was vibrated with a white noise signal. The full-field result as well as the displacement of a single point on the wing over time was then obtained using ARAMIS® software, a DIC technique-based software. From the temporal displacement of a single point signal in the time domain, we performed fast Fourier transform to obtain the frequency response function (FRF). The spectrum averaging technique and Savitzky-Golay filter were used to reduce the noise. Also, the natural frequencies and damping factors were determined from smoothed FRF. Finally, the mode shapes were measured using DIC at the pre-measured natural frequency.

How Angular Velocity Features and Different Gyroscope Noise Types Interact and Determine Orientation Estimation Accuracy

Abstract: In human movement analysis, 3D body segment orientation can be obtained through the numerical integration of gyroscope signals. These signals, however, are affected by errors that, for the case of micro-electro-mechanical systems, are mainly due to: constant bias, scale factor, white noise, and bias instability. The aim of this study is to assess how the orientation estimation accuracy is affected by each of these disturbances, and whether it is influenced by the angular velocity magnitude and 3D distribution across the gyroscope axes. Reference angular velocity signals, either constant or representative of human walking, were corrupted with each of the four noise types within a simulation framework. The magnitude of the angular velocity affected the error in the orientation estimation due to each noise type, except for the white noise. Additionally, the error caused by the constant bias was also influenced by the angular velocity 3D distribution. As the orientation error depends not only on the noise itself but also on the signal it is applied to, different sensor placements could enhance or mitigate the error due to each disturbance, and special attention must be paid in providing and interpreting measures of accuracy for orientation estimation algorithms.

Effect of external noise on the hysteresis characteristics of a thermoacoustic system

Abstract: We present the effect of noise on the hysteresis characteristics of a prototypical thermoacoustic system, a horizontal Rijke tube. As we increase the noise intensity, we find that the width of the hysteresis zone decreases. However, we find that the rate of decrease in hysteresis width is constant for all the mass flow rates considered in the present study. We also show that the subcritical transition observed in the absence of noise is no longer discernible once the intensity of noise is above a threshold value and the transition appears to be continuous. We compare our experimental observations with the results obtained from a numerical model perturbed with additive Gaussian white noise and we find a qualitative agreement between the experimental and the numerical results.