Multiplicative Noise Components Research Articles

Skeleting of Low-Contrast Noisy Halftone Images

The problem of forming the skeletons of halftone images with two-mode brightness histograms under conditions of changing contrast and noise is considered. On such histograms, one mode corresponds to the objects, and the other to the background. Thanks to this feature, images are relatively easy to binarize and then skeletonize. The skeleton of a region uniform in brightness is a set of thin (limited by one-pixel) connected lines enclosed within this region and compactly describing its structure. Under conditions of high contrast and low noise on the original halftone image, binary skeletonization algorithms are widely used. They are relatively simple and can be resistant to multiplicative noise that appears at the boundaries of the regions after binarization. However, when the contrast is reduced and the noise of the original halftone image is increased, the skeletons formed by such algorithms are destroyed under the influence of additive noise, which manifests itself in the depth of the regions of the skeletonized binary image. To reduce skeletonization errors in such cases, algorithms based on preliminary low-pass filtering of the original grayscale image are used. To increase the stability of the skeletons of halftone images with a two-mode brightness histogram to noise, the article proposes a skeletonization model that takes into account the presence of multiplicative and additive noise components in a binary skeletonized image. Taking this model into account, a skeletonization algorithm has been developed, which takes into account the distortions in the shapes of the areas of the skeletonized binary image as a result of low-frequency filtering of the original halftone image and allows to reduce errors in the skeletonization of halftone images.

Stochastic modeling of the cutting force in turning processes

The main goal of this study is to introduce a stochastic extension of the already existing cutting force models. It is shown through orthogonal cutting force measurements how stochastic processes based on Gaussian white noise can be used to describe the cutting force in material removal processes. Based on these measurements, stochastic processes were fitted on the variation of the cutting force signals for different cutting parameters, such as cutting velocity, chip thickness, and rake angle. It is also shown that the variance of the measured force signal is usually around 4–9% of the average value, which is orders of magnitudes larger than the noise originating from the measurement system. Furthermore, the force signals have Gaussian distribution; therefore, the cutting force model can be extended by means of a multiplicative noise component.

Rate of convergence to equilibrium of fractional driven stochastic differential equations with rough multiplicative noise

We investigate the problem of the rate of convergence to equilibrium for ergodic stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H\in(1/3,1)$ and multiplicative noise component $\sigma$. When $\sigma$ is constant and for every $H\in(0,1)$, it was proved in [Ann. Probab. 33 (2005) 703–758] that, under some mean-reverting assumptions, such a process converges to its equilibrium at a rate of order $t^{-\alpha}$ where $\alpha\in(0,1)$ (depending on $H$). In [Ann. Inst. Henri Poincaré Probab. Stat. 53 (2017) 503–538], this result has been extended to the multiplicative case when $H>1/2$. In this paper, we obtain these types of results in the rough setting $H\in(1/3,1/2)$. Once again, we retrieve the rate orders of the additive setting. Our methods also extend the multiplicative results of [Ann. Inst. Henri Poincaré Probab. Stat. 53 (2017) 503–538] by deleting the gradient assumption on the noise coefficient $\sigma$. The main theorems include some existence and uniqueness results for the invariant distribution.

Analysis of measurement data subject to additive and multiplicative effects

Many calibration problems in metrology involve fitting a model to measurement data representing the response of a system. The standard assumption about the measurement system is that the random effects associated with the measurements are drawn from the same distribution. In practice however, the uncertainty associated with the measurements may depend on the magnitude of the response being measured. For example, the measurement of displacement using laser interferometry follows such a model in which the uncertainty has a dependence on length due to the uncertainty associated with the refractive index of the air. For such systems, the model is inherently nonlinear for which standard approaches such linear least-squares estimation provide only approximate solutions.This paper describes a Bayesian approach for analysing such data. The data is modelled as a linear or non-linear response subject to additive and multiplicative noise components. We assume that prior, possibly vague, information about the variances associated with additive and multiplicative noise components is given in terms of Gamma distributions. The Bayesian posterior distribution for such models cannot be expressed analytically in closed form and a Metropolis-Hastings Markov chain Monte Carlo algorithm is used to sample from the posterior distribution. This method is illustrated on data relating to the radioactive decay of Pb211.

Self-organisation of random oscillators with Lévy stable distributions

A novel possibility of self-organized behaviour of stochastically driven oscillators is presented. It is shown that synchronization by Lévy stable processes is significantly more efficient than that by oscillators with Gaussian statistics. The impact of outlier events from the tail of the distribution function was examined by artificially introducing a few additional oscillators with very strong coupling strengths and it is found that remarkably even one such rare and extreme event may govern the long term behaviour of the coupled system. In addition to the multiplicative noise component, we have investigated the impact of an external additive Lévy distributed noise component on the synchronisation properties of the oscillators.

Extremes in dynamic-stochastic systems.

Extreme events capture the attention and imagination of the general public. Extreme events, especially meteorological and climatological extremes, cause significant economic damages and lead to a significant number of casualties each year. Thus, the prediction of extremes is of obvious importance. Here, I will survey the predictive skill and the predictability of extremes using dynamic-stochastic models. These dynamic-stochastic models combine deterministic nonlinear dynamics with a stochastic component, which consists potentially of both additive and multiplicative noise components. In these models, extremes are created by either the nonlinear dynamics, multiplicative noise, or additive heavy-tailed noises. These models naturally capture the observed clustering of extremes and can be used for the prediction of extremes.

A simple approach to quantifying the noise–ENSO interaction. Part II: the role of coupling between the warm pool and equatorial zonal wind anomalies

Stochastic forcing has been used conceptually to explain ENSO irregularity. More recently, the concept of state-dependent (multiplicative) stochastic forcing has been explored as an explanation of a number of ENSO properties. By calculating the state-dependence factor of ENSO zonal wind stress noise forcing on SST, we are able to separate the additive and multiplicative components of the wind stress noise forcing of ENSO. Spatially, the months with large additive or multiplicative components all resemble previous studies on westerly wind bursts. They differ from each other in that the wind stresses are significantly stronger during months with a large multiplicative noise component. It is further shown that when the multiplicative noise component is large, there have been large values of the wind stress noise in the preceding months. This is not true of the months when the additive component is large. The multi-month growth of the wind stress from the multiplicative noise process is shown to be related to an eastward migration of the western Pacific Warm Pool, which is coupled to the wind stress through convection. This process is shown to be significantly weakened in a climate model when the ocean and atmosphere are uncoupled.

Rate of convergence to equilibrium of fractional driven stochastic differential equations with some multiplicative noise

We investigate the problem of the rate of convergence to equilibrium for ergodic stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H\in (1/3,1)$ and multiplicative noise component $\sigma$. When $\sigma$ is constant and for every $H\in (0,1)$, it was proved in [19] that, under some mean-reverting assumptions, such a process converges to its equilibrium at a rate of order $t^{-\alpha}$ where $\alpha \in (0,1)$ (depending on $H$). In [11], this result has been extended to the multiplicative case when $H>1/2$. In this paper, we obtain these types of results in the rough setting $H\in (1/3,1/2)$. Once again, we retrieve the rate orders of the additive setting. Our methods also extend the multiplicative results of [11] by deleting the gradient assumption on the noise coefficient $\sigma$. The main theorems include some existence and uniqueness results for the invariant distribution.

Homomorphic filtering textural analysis technique to reduce multiplicative noise in the 11Oba nano-doped liquid crystalline compounds

The compound undecyloxy benzoic acid (11Oba) exhibits nematic and smectic-C phases while a nano-doped undecyloxy benzoic acid with ZnO exhibits the same nematic and smectic-C phases with reduced clearing temperature as expected. The doping is done with 0.5% and 1% ZnO molecules. The clearing temperatures are reduced by approximately 4 ° and 6 °, respectively (differential scanning calorimeter data). While collecting the images from a polarizing microscope connected with hot stage and camera, the illumination and reflectance combined multiplicatively and the image quality was reduced to identify the exact phase in the compound. A novel technique of homomorphic filtering is used in this manuscript through which multiplicative noise components of the image are separated linearly in the frequency domain. This technique provides a frequency domain procedure to improve the appearance of an image by gray level range compression and contrast enhancement.

THE MULTIPLICATIVE NOISE COMPONENTS OF ISOMETRIC FORCE FLUCTUATIONS

The experiment tested the relative contribution of additive and multiplicative noise components in isometric force fluctuations. We implemented the Hilbert–Huang transform to analyze variability in the steady state region of isometric force time series generated by participants in three adult age categories: (1) young (20–24 yrs); (2) old (60–69 yrs); and older-old (75–90 yrs). Each participant generated isometric force output in response to constant target force levels (5–40% maximum voluntary contraction). The empirical mode decomposition component of the Hilbert–Huang transform was applied to each isometric force time series resulting in a set of intrinsic mode functions (IMFS). The amplitude modulation envelopes of the IMFS obtained from the modulus of the Hilbert transform were random sequences. These random sequences were the source of the multiplicative noise. Analyses showed significant age group differences in the multiplicative noise structure of the force output. The results provide preliminary evidence that multiplicative noise dominates additive noise in isometric force output and can discriminate among the force fluctuations of healthy adult participants of different ages.

Pseudo-Maximum Likelihood Estimation of ballistic missile precession frequency

In order to estimate a ballistic missile precession frequency, which is an important feature parameter in ballistic target recognition, we firstly establish the dynamic Radar Cross Section (RCS) signal model for a conical ballistic missile warhead with precession motion. Scintillation which is an important factor that cannot be ignored in radar measurement is taken into account in the model establishment, and modeled either as a log-normal or chi-square multiplicative noise. The distribution of obtained RCS signal is non-Gaussian and cannot be obtained in closed-form. Hence, the exact Maximum Likelihood Estimation (MLE) of the pertinent parameter, the missile precession frequency, is untractable. In the paper, we propose three pseudo-MLE approaches to estimate the parameter of missile precession frequency. The first approach ignores the multiplicative noise in the measured RCS. The second approach ignores the additive noise (i.e., assuming the infinite signal-to-noise ratio (SNR)). The third approach enforces a Gaussian distribution on both additive and multiplicative noise components. The Cramér–Rao lower bound (CRLB) corresponding to the maximum SNR scenario is derived. Simulations indicate that accounting for the multiplicative noise in the estimation significantly improves estimation performance, and also show the validation and robustness of the proposed methods.

Reduced-Order Filter Design for Discrete-Time Systems Corrupted with Multiplicative Noise

The paper presents an H∞ -type estimation problem for discrete-time systems subject to multiplicative noise. Such systems naturally arise in many applications in aerospace engineering, including navigation, communications, estimation of target states, imagery. In this paper the attention is focused on determining a design method of a fixed (reduced) order filter. It is shown that if the system output is not corrupted with multiplicative noise then the existence of such filter is equivalent with the feasibility of a specific system of linear matrix inequalities. In the case when the output includes multiplicative noise components the existence conditions depend on the solutions of a system of linear matrix inequalities subject to a rank minimization condition. For the considered problem the rank constraint can be solved as a semi-definite programming problem using a particular affine transformation.

Arbitrary-order corrections for finite-time drift and diffusion coefficients

We address a standard class of diffusion processes with linear drift and quadratic diffusion coefficients. These contributions to dynamic equations can be directly drawn from data time series. However, real data are constrained to finite sampling rates and therefore it is crucial to establish a suitable mathematical description of the required finite-time corrections. Based on Itô-Taylor expansions, we present the exact corrections to the finite-time drift and diffusion coefficients. These results allow to reconstruct the real hidden coefficients from the empirical estimates. We also derive higher-order finite-time expressions for the third and fourth conditional moments that furnish extra theoretical checks for this class of diffusion models. The analytical predictions are compared with the numerical outcomes of representative artificial time series.

Analysis of the problems of statistical estimations in stochastic sources of discrete electron fluxes

Using computer simulation of an experiment on measuring statistical characteristics of electron fluxes, we study the mechanism of appearance of the modulation (in particular multiplicative) noise component due to the discrete nature of electron fluxes in vacuum and analytical devices. It is shown that the presence of both uncorrelated and correlated multiplicative noise in electron devices and inertia of circuits for recording of instantaneous values of the electron current significantly change statistical properties of the measured fluctuation processes. In most cases, the above-mentioned factors can introduce noticeable errors during experimental estimations of statistical distributions in solids, in particular energy distributions of emitted electrons, if the existing measurement techniques are used.

Dynamic two state stochastic models for ecological regime shifts

AbstractA simple non‐linear stochastic two state, discrete‐time model is presented. The interaction between benthic and pelagic vegetation in aquatic ecosystems subject to changing external nutrient loading is described by the non‐linear functions. The dynamical behavior of the deterministic part of the model illustrates that hysteresis effect and regime shifts can be obtained for a limited range of parameter values only. The effect of multiplicative noise components entering at different levels of the model is presented and discussed. Including noise leads to very different results on the stability of regimes, depending on how the noise propagates through the system. The dynamical properties of a system should therefore be described through propagation of the state distributions rather than the state means and consequently, stochastic models should be compared in a probabilistic framework. Copyright © 2008 John Wiley & Sons, Ltd.

Design of the optimal sector device and determination of its parameters in gas electron diffraction

This work presents a way to select the optimal form of the sector lobe and practical algorithms to determine the sector function of the device in use. Knowledge of the sector function enhances the quality of drawing a background line and ensures the division of multiplicative and additive noise components, thus increasing the reliability of structural parameters determined by gas electron diffraction.

Extraneous scattering and its discrimination in gas electron diffraction

The division algorithm for additive and multiplicative noise components of the electron scattering intensity is proposed in the work. The procedure presented provides a substantial improvement in experimental data processing in comparison with the traditional method used by Russian research groups. A comparison of the additive noise with the simulated residual gas scattering shows that it is this scattering that is largely responsible for the strange contribution to the measured diffraction pattern.

On the Extension of Multidimensional Speckle Noise Model From Single-Look to Multilook SAR Imagery

Speckle noise represents one of the major problems when synthetic aperture radar (SAR) data are considered. Despite the fact that speckle is caused by the scattering process itself, it must be considered as a noise source due to the complexity of the scattering process. The presence of speckle makes data interpretation difficult, but it also affects the quantitative retrieval of physical parameters. In the case of one-dimensional SAR systems, speckle is completely determined by a multiplicative noise component. Nevertheless, for multidimensional SAR systems, speckle results from the combination of multiplicative and additive noise components. This model has been first developed for single-look data. The objective of this paper is to extend the single-look data model to define a multilook multidimensional speckle noise model. The asymptotic analysis of this extension, for a large number of averaged samples, is also considered to assess the model properties. Details and validation of the multilook multidimensional speckle noise model are provided both theoretically and by means of experimental SAR data acquired by the experimental synthetic aperture radar system, operated by the German Aerospace Center

Blind Equalization of Dispersive Fast Fading Ricean Channels Via the EMV Algorithm

A blind maximum likelihood equalization method is proposed for frequency selective fast fading Ricean channels. This method employs the expectation-maximization Viterbi algorithm (EMVA) developed in for blind channel estimation and signal detection. Since the Viterbi algorithm (VA) is used to execute the E-phase of an expectation-maximization (EM) iteration, it requires that the observed sequence can be modelled as a finite-state hidden Markov process. We develop a hidden Markov model for frequency selective fast fading Ricean channels, so that the observed process can be viewed as the noisy output of a finite state machine (FSM), to which the VA is applicable. The EMVA is then employed to obtain a blind maximum likelihood estimate of the specular part of the channel and, for one special case, of a noise parameter measuring the total power of the additive and multiplicative channel noise components. Simulation results are presented which show that the EMVA achieves an accurate estimate of the channel specular part and has an error rate performance close to that of the maximum likelihood detector based on true parameters for the given FSM model.

Interpreting wind-driven Southern Ocean variability in a stochastic framework

A stochastic model is derived from wind stress and bottom pressure gauge data to examine the response of the Antarctic Circumpolar Current (ACC) transport to wind stress forcing. A general method is used to estimate the drift and diffusion coefe cients of a continuous stationary Markovian system. As a e rst approximation, the response of the ACC to wind stress forcing can be described by a multivariate Ornstein-Uhlenbeck process: Gaussian red noise wind stress drives the evolution of the ACC transport, which is damped by a linear drag term. The model indicates that about 30( 610)% of ACC variability is directly driven by the wind stress. This stochastic model can serve as a null hypothesis for studies of wind driven ACC variability. A more accurate stochastic description of the wind stress over the Southern Ocean requires a multiplicative noise component. The variability of the wind stress increases approximately linearly with increasing wind stress values. A multiplicative stochastic process generates a power-law distribution rather than a Gaussian distribution. A simple stochastic model shows that non-Gaussian forcing could have a signie cant impact on the velocity (or transport) probability density functions (PDFs) of the wind-driven circulation. The net oceanic damping determines whether the distribution of the oceanic e ow is Gaussian (small damping) or resembles the distribution of the atmospheric forcing (large damping).