Nonlinear Noise Model Research Articles

Generalized signal-dependent noise model and parameter estimation for natural images

The goal of this paper is to propose a generalized signal-dependent noise model that is more appropriate to describe a natural image acquired by a digital camera than the conventional Additive White Gaussian Noise model widely used in image processing. This non-linear noise model takes into account effects in the image acquisition pipeline of a digital camera. In this paper, an algorithm for estimation of noise model parameters from a single image is designed. Then the proposed noise model is applied with the Local Linear Minimum Mean Square Error filter to design an efficient image denoising method.

A Fully Nonlinear Compact Modeling Approach for High-Frequency Noise in Large-Signal Operated Microwave Electron Devices

A technology-independent, inherently nonlinear approach is proposed for the compact modelling of high-frequency noise in microwave transistors under large-signal operating conditions. For the compact nonlinear noise model formulation we assume that noise generation can be described by a suitable set of distributed stochastic processes perturbing a very general, non-quasi-static deterministic description of the electron device, in accordance with the strategies adopted in physics-based methods for the choice and exploitation of microscopic diffusion noise sources. The propagation of the internal distributed noise sources up to the intrinsic device terminals leads to a set of non-stationary, correlated equivalent noise generators, nonlinearly controlled by the instantaneous large-signal working point of the device. Starting from a first formulation for the generators, formally derived from a physics-based description of the noise generation mechanisms widely adopted in distributed numerical modeling, mild approximations provide a fully behavioral representation that can be empirically extracted on the basis of measurement data only, and can be easily implemented into commercial computer-aided design tools by means of conventional, uncorrelated noise sources. As far as small-signal (i.e., linear) bias-dependent operation is concerned, it is shown how well-known, widely applied compact models for high-frequency noise can be considered as linearized special cases of the proposed approach. For a full validation, experimental examples are provided, both in small- and large-signal operation, for a GaAs-pHEMT, by considering the case study of a broad-band low-noise amplifier progressively driven into nonlinear regime by an increasing power interferer.

Modeling Nonlinear White Noise in GaN HEMT Devices

Abstract This paper compares new bias-dependent descriptions for the Pucel and Pospieszalski noise models for GaN HEMT devices. It is proposed to replace the traditional descriptions of the noise sources by general noise powers linked to the drain current. A well-behaved bias dependence of the new parameters is observed for both models the new approach reduces uncertainty in the nonlinear noise model extraction. Finally, the performance of the bias-dependent noise models under nonlinear excitation is investigated and it can be shown that Pucel and Pospieszalski models yield comparably good accuracy in noise prediction.

An analytical formulation for phase noise in MEMS oscillators.

In recent years, there has been much interest in the design of low-noise MEMS oscillators. This paper presents a new analytical formulation for noise in a MEMS oscillator encompassing essential resonator and amplifier nonlinearities. The analytical expression for oscillator noise is derived by solving a second-order nonlinear stochastic differential equation. This approach is applied to noise modeling of an electrostatically addressed MEMS resonator-based square-wave oscillator in which the resonator and oscillator circuit nonlinearities are integrated into a single modeling framework. By considering the resulting amplitude and phase relations, we derive additional noise terms resulting from resonator nonlinearities. The phase diffusion of an oscillator is studied and the phase diffusion coefficient is proposed as a metric for noise optimization. The proposed nonlinear phase noise model provides analytical insight into the underlying physics and a pathway toward the design optimization for low-noise MEMS oscillators.

Nonlinear time‐series modeling of unconfined groundwater head

AbstractThis paper presents a nonlinear transfer function noise model for time‐series modeling of unconfined groundwater hydrographs. The motivation for its development was that existing groundwater time‐series models were unable to simulate large recharge events and multiyear droughts. This was because existing methods do not partition rainfall to runoff and do not account for nonlinear soil water drainage. To account for these nonlinear processes, a vertically integrated soil moisture module was added to an existing transfer function noise model. The soil moisture module has a highly flexible structure that allowed 84 different forms to be built. Application of the time‐series model requires numerical calibration of parameters for the transfer functions, noise model and, for the nonlinear models, the soil moisture module. This was undertaken using the Covariance Matrix Adaptation Evolutionary Strategy (CMA‐ES) global calibration scheme. However, reproducible calibration to the global optima was challenging and a number of modifications were required to the transfer function noise model. In trialing the 84 nonlinear models and 2 linear models, each was applied to eleven observation bores within a paired catchment study area in Great Western, Victoria, Australia. In comparison with existing groundwater hydrograph time‐series models, the proposed nonlinear time‐series model performed significantly better at all observation bores during calibration and evaluation periods. Both the linear and nonlinear models were also used to quantify the impact of revegetation within the paired catchment; however, results were inconclusive, which is likely due to time‐series data for the state of the revegetation being unavailable. By analyzing the application of 84 nonlinear models to each bore, an optimal structure for the soil moisture module was identified. It is unlikely, however, that this model structure would be appropriate for all climates and geologies. To encourage further investigations, open‐source code for the highly flexible groundwater time‐series modeling framework is available and we invite others to develop new models.

Joint non-Gaussian denoising and superresolving of raw high frame rate videos.

High frame rate cameras capture sharp videos of highly dynamic scenes by trading off signal-noise-ratio and image resolution, so combinational super-resolving and denoising is crucial for enhancing high speed videos and extending their applications. The solution is nontrivial due to the fact that two deteriorations co-occur during capturing and noise is nonlinearly dependent on signal strength. To handle this problem, we propose conducting noise separation and super resolution under a unified optimization framework, which models both spatiotemporal priors of high quality videos and signal-dependent noise. Mathematically, we align the frames along temporal axis and pursue the solution under the following three criterion: 1) the sharp noise-free image stack is low rank with some missing pixels denoting occlusions; 2) the noise follows a given nonlinear noise model; and 3) the recovered sharp image can be reconstructed well with sparse coefficients and an over complete dictionary learned from high quality natural images. In computation aspects, we propose to obtain the final result by solving a convex optimization using the modern local linearization techniques. In the experiments, we validate the proposed approach in both synthetic and real captured data.

Nonlinear Model of Image Noise: An Application on Computed Tomography including Beam Hardening and Image Processing Algorithms

This paper proposes a more inclusive statistical model for predicting image noise in Computed Tomography (CT), associated with scanning factors, considering the effect of beam hardening and image processing filters. It is based on power functions where the levels of the parameters will determine the rate of noise variation with respect to a given scanning factor. It includes the influence of tube potential, tube current, slice thickness, Field of View (FOV), reconstruction methods and post-processing filters. To validate the model, tomographic measurements were made by using a PMMA phantom that simulates paediatric head and adult abdomen, a PET bottle was used to simulate the head of the new-born. The influence of ROI (Region Of Interest) size over nonlinear model parameters was analysed, and high variations of powers of attenuation and FOV were found depending on ROI size. A nonlinear robust regression method was used. The validation was performed graphically by weighted residual analysis. A nonlinear noise model was obtained with an adjusted coefficient of determination for ROI sizes between 10% and 70% of the phantom diameter or FOV. The model confirms the significance of the tube current, slice thickness and beam hardening effect on image. The process of estimation of the parameters of the model by Nonlinear Robust Regression turned out to be optimal.

Online Spot Volatility-Estimation and Decomposition with Nonlinear Market Microstructure Noise Models

A technique for online estimation of spot volatility for high-frequency data is developed. The algorithm works directly on the transaction data and updates the volatility estimate immediately after the occurrence of a new transaction. Furthermore, a nonlinear market microstructure noise model is proposed that reproduces several stylized facts of high-frequency data. A computationally efficient particle filter is used that allows for the approximation of the unknown efficient prices and, in combination with a recursive EM algorithm, for the estimation of the volatility curve. We neither assume that the transaction times are equidistant nor do we use interpolated prices. We also make a distinction between volatility per time unit and volatility per transaction and provide estimators for both. More precisely we use a model with random time change where spot volatility is decomposed into spot volatility per transaction times the trading intensity--thus highlighting the influence of trading intensity on volatility. Copyright The Author, 2013. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com, Oxford University Press.

The NOPTILUS project: Autonomous Multi-AUV Navigation for Exploration of Unknown Environments

Current multi-AUV systems are far from being capable of fully autonomously taking over real-life complex situation-awareness operations. As such operations require advanced reasoning and decision-making abilities, current designs have to heavily rely on human operators. The involvement of humans, however, is by no means a guarantee of performance; humans can easily be over-whelmed by the information overload, fatigue can act detrimentally to their performance, properly coordinating vehicles actions is hard, and continuous operation is all but impossible. Within the European funded project NOPTILUS we take the view that an effective fully-autonomous multi-AUV concept/system, is capable of overcoming these shortcomings, by replacing human-operated operations by a fully autonomous one. In this paper, we present a new approach that is able to efficiently and fully-autonomously navigate a team of AUVs when deployed in exploration of unknown static and dynamic environments towards providing accurate static/dynamic maps of the environment. Additionally to achieving to efficiently and fully-autonomously navigate the AUV team, the proposed approach possesses certain advantages such as its extremely computational simplicity and scalability, and the fact that it can very straightforwardly embed and type of physical or other constraints and limitations (e.g., obstacle avoidance, nonlinear sensor noise models, localization fading environments, etc).

On the correct modeling of semiconductor optical amplifier RIN and phase noise for optical phase shift keyed communication systems

Phase modulation schemes are attracting much interest for use in ultra-fast optical communication systems because they are much less affected by fiber nonlinearities than conventional modulation formats. Semiconductor optical amplifiers (SOAs) can be used to amplify and process phase modulated signals. However, existing SOA nonlinear phase noise (NLPN) models are simplistic and, sometimes, inaccurate. It is, therefore, important to correctly model their behavior since NLPN is the main drawback in these applications. In this paper we show that a more accurate model can be used leading to simple nonlinear noise expressions at the SOA output of differential phase shift keying systems. To demonstrate the utility of this model, we have used it to calculate the optical signal to noise ratio penalties introduced by a power booster SOA and the first inline amplifier of a 40 Gb/s NRZ-DQPSK single channel link. The model parameters have been estimated from measurements taken of a commercial SOA.

Investigation of Phase Noise Generation in Microwave Electron Devices Operating in Nonlinear Regime Exploiting a Flexible Load– and Source–Pull Oscillating Setup

In this paper, we present a flexible measurement setup for the characterization of the phase noise (PN) and frequency stability of microwave electron devices operating under nonlinear oscillating conditions. The setup embeds the device-under-test (DUT) within a feedback loop, and forces it into a large signal (LS) oscillating regime, by controlling the loop amplitude and phase. The DUT input and output terminations are also controlled, by exploiting load- and source-pull capabilities. By exploiting this setup, we demonstrate that the PN performance of microwave oscillators can be strongly affected by the device nonlinear RF working regime. As well known, the oscillator PN is mainly related to the frequency stability of the circuit and the active device low-frequency noise up-conversion to RF mechanisms. By using measurements performed with the proposed setup, it is shown that these aspects depend also on the device LS operating conditions; hence, the dynamic LS load line and the amplifying class of operation have a significant role for the oscillator PN. The experimental results described in the paper, along with the analyses proposed by using simulations, are in accordance with recently published nonlinear noise modeling approaches based on cyclostationary noise sources. The investigation performed by means of the setup can provide information for both the design of low-phase-noise (LPN) oscillators and the parameter extraction and validation of nonlinear noise models of electron devices. Furthermore, this setup is also proposed as a tool for the evaluation of power amplifier PN when a dedicated residual phase noise measurement system is not available.

An Empirical Bipolar Device Nonlinear Noise Modeling Approach for Large-Signal Microwave Circuit Analysis

An empirical bipolar transistor nonlinear noise model for the large-signal (LS) noise analysis of microwave circuits is described. The model is derived according to the charge-controlled nonlinear noise behavioral modeling approach, and includes nonlinearly controlled equivalent noise (EN) generators describing the low-frequency (LF) noise up-conversion encountered in LS RF operation. LS-modulated shot-noise sources and parametric LF noise in parasitic resistors are also taken into account for improved model accuracy. Details for the implementation of the proposed cyclostationary EN generators in the framework of a computer-aided design tool are presented. As an application example, a simplified version of the proposed nonlinear noise model for two GaInP-GaAs HBTs has been formulated and empirically characterized on the basis of both bias-dependent LF noise and phase-noise measurements. Measured and simulated noise performance of a monolithic voltage-controlled oscillator over a set of different operating conditions is shown for the validation of the proposed approach

On the active periods of nonlinear Shot Noise

We study the temporal ‘on-and-off’ structure of the recently introduced nonlinear Shot Noise model [I. Eliazar, J. Klafter, PNAS 102 (2005) 13779; I. Eliazar, J. Klafter, Nonlinear shot noise: Lévy, Noah, & Joseph, Physica A (2006), to appear], in which: (i) shots of random magnitudes ‘bombard’ a system stochastically in time; (ii) the magnitudes of ‘incoming’ shots decay to zero nonlinearly; and, (iii) the overall effect of the shots on the system is additive. When the shot-inflow and shot-decay satisfy certain conditions, the resulting Shot Noise alternates randomly between ‘active periods’ (in which the noise is ‘on’) and ‘silent periods’ (in which noise is ‘off’). The statistical properties of the ‘active’ and ‘silent’ periods are analyzed, and the resulting ‘on-and-off’ Shot Noise structure is explored. Explicit formulae for means, variances, Laplace transforms, and other statistics are derived in closed-form. Based on this analysis, Shot Noise systems are categorized into three classes: transient, null-recurrent, and recurrent; and, these classes are characterized both analytically and probabilistically. Within the null-recurrent class, systems whose ‘active periods’ are governed by heavy-tailed probability distributions are further characterized.

Nonlinear device noise models: Satisfying the thermodynamic requirements

This paper proposes three tests to determine whether a given nonlinear device noise model is in agreement with accepted thermodynamic principles. These tests are applied to several models. One conclusion is that the standard Gaussian noise models for nonlinear devices predict thermodynamically impossible circuit behavior: those models should be abandoned. But the nonlinear shot-noise model predicts thermodynamically acceptable behavior under a constraint derived here. Further, this constraint specifies the current noise amplitude at each operating point from knowledge of the device /spl upsi/-i curve alone. This paper shows how the thermodynamic requirements can be reduced to concise mathematical tests, involving no approximations, for the Gaussian and shot-noise models.

Improved HEMT model for low phase-noise InP-based MMIC oscillators

This paper focuses on two modeling aspects to improve the accuracy of low phase-noise monolithic-microwave integrated-circuit (MMIC) oscillator design. Up until now, the modeling of InP-based high electron mobility transistors (HEMTs) has mainly been limited to the representation of small-signal and thermal noise behavior. In this paper, we present a scaleable nonlinear and bias-dependent low-frequency (LF) noise model.

Noise modeling in MESFET and HEMT mixers using a uniform noisy line model

The aim of this paper is to present a noise model which predicts the noise performance of MESFET and HEMT mixers. The conversion and noise correlation matrices of a FET mixer are calculated using a uniform nonlinear noisy active line concept to describe the FET. This calculation is based on a perturbation analysis of the large-signal noiseless steady state, making it a microscopic nonlinear noise model. This method is applied to the case of a hot HEMT gate mixer and we show that the theoretical results are in agreement with experimental data.

General noise analysis of nonlinear microwave circuits by the piecewise harmonic-balance technique

This paper presents a self-consistent set of algorithms for the numerical computation of noise effects in forced and autonomous nonlinear microwave circuits. The analysis relies upon the piecewise harmonic-balance method, and thus retains all the peculiar advantages of this technique, including general-purposeness in the widest sense. The noise simulation capabilities include any kind of forced or autonomous nonlinear circuit operated in a time-periodic large-signal steady state, as well as microwave mixers of arbitrary topology. The limitations of the traditional frequency-conversion approach to noise analysis are overcome. The analysis takes into account the thermal noise generated in the passive subnetwork, the noise contributions of linear and nonlinear active devices, and the noise injected by sinusoidal driving sources of known statistical properties. The nonlinear noise models of two representative families of microwave devices (FET's/HEMT's and Schottky-barrier diodes) are discussed in detail, and several applications are illustrated.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>