Additive Noise Research Articles

3D-Oculography: New Method of Determination of Human Gaze Point Position in Space

INTRODUCTION: Oculography — a method of recording movement of eyeballs of a human or animal by analyzing changes in electrical potentials recorded by two electrodes fixed on skin near the eye socket is used to solve various problems. Among them are the determination of pronounced nystagmus, of characteristic changes of oculomotor reactions in different conditions of observing video images. Of interest is the determination of the position of gaze point (GP) and of the area of increased attention in three-dimensional space. This information is associated with the cognitive system of the observer and is of interest not only to physiologists, but also to specialists of related fields. . AIM: To experimentally prove the effectiveness of the developed method of 3D-oculography providing determination of the GP position in space. MATERIALS AND METHODS: The possibility of restoring GP position based on the analysis of recorded oculograms even in the presence of additive noise induced by the external electromagnetic fields, is proven by the numeric modeling method. Direct experimental studies were conducted with recording oculograms of a human observer on a previously verified equipment. A ZB-2 oculograph was used, the data obtained were verified by the method of average values. RESULTS: The obtained modeling results permitted to determine the maximal values of dispersion of additive noise and amplitude shifts of signals, which make possible satisfactory restoration of the coordinates of the GP and parameters of its movement trajectory. The qualitative correspondence of the experimental results to the results of numerical modeling was proven. The correspondence between trajectories of the observed object moving in space and trajectories of GP movement synthesized from counts of recorded oculograms was confirmed. CONCLUSION: Multichannel record of oculographic signals permits restoring parameters of the GP trajectory. Creating systems for recording these signals requires minimization of the noise level. An increase in dispersion of the noise component of the signal leads to most significant errors in calculating the coordinates of trajectory points.

On the functional regression model and its finite-dimensional approximations

AbstractThe problem of linearly predicting a scalar response Y from a functional (random) explanatory variable $$X=X(t),\ t\in I$$ X = X ( t ) , t ∈ I is considered. It is argued that the term “linearly” can be interpreted in several meaningful ways. Thus, one could interpret that (up to a random noise) Y could be expressed as a linear combination of a finite family of marginals $$X(t_i)$$ X ( t i ) of the process X, or a limit of a sequence of such linear combinations. This simple point of view (which has some precedents in the literature) leads to a formulation of the linear model in terms of the RKHS space generated by the covariance function of the process X(t). It turns out that such RKHS-based formulation includes the standard functional linear model, based on the inner product in the space $$L^2[0,1]$$ L 2 [ 0 , 1 ] , as a particular case. It includes as well all models in which Y is assumed to be (up to an additive noise) a linear combination of a finite number of linear projections of X. Some consistency results are proved which, in particular, lead to an asymptotic approximation of the predictions derived from the general (functional) linear model in terms of finite-dimensional models based on a finite family of marginals $$X(t_i)$$ X ( t i ) , for an increasing grid of points $$t_j$$ t j in I. We also include a discussion on the crucial notion of coefficient of determination (aimed at assessing the fit of the model) in this setting. A few experimental results are given.

Enhanced Discrete Wavelet Transform–Non-Local Means for Multimode Fiber Optic Vibration Signal

Real-time monitoring of heartbeat signals using multimode fiber optic microvibration sensing technology is crucial for diagnosing cardiovascular diseases, but the heartbeat signals are very weak and susceptible to noise interference, leading to inaccurate diagnostic results. In this paper, a combined enhanced discrete wavelet transform (DWT) and non-local mean estimation (NLM) denoising method is proposed to remove noise from heartbeat signals, which adaptively determines the filtering parameters of the DWT-NLM composite method using objective noise reduction quality assessment metrics by denoising different ECG signals from multiple databases with the addition of additive Gaussian white noise (AGW) with different signal-to-noise ratios (SNRs). The noise reduction results are compared with those of NLM, enhanced DWT, and conventional DWT combined with NLM method. The results show that the output SNR of the proposed method is significantly higher than the other methods compared in the range of −5 to 25 dB input SNR. Further, the proposed method is employed for noise reduction of heartbeat signals measured by fiber optic microvibration sensing. It is worth mentioning that the proposed method does not need to obtain the exact noise level, but only the adaptive filtering parameters based on the autocorrelation nature of the denoised signal. This work greatly improves the signal quality of the multimode fiber microvibration sensing system and helps to improve the diagnostic accuracy.

TPRT: a trajectory publishing scheme for the Internet of Vehicles based on radix tree

Abstract The location and trajectory information generated in the Internet of Vehicles (IoV) provides sufficient data support for road network planning. However, there is much sensitive information in these data, and publishing them directly will lead to serious privacy leakage risks. Therefore, this paper proposes a trajectory publishing scheme for the Internet of Vehicles based on radix tree (TPRT). Firstly, the trajectory data are divided into multiple location planes based on timestamps and processed using clustering and generalization. This approach addresses the issue of real-life trajectory data having almost no identical prefixes, making it more suitable for storage in radix tree. Then, the directed graph and the shortest path algorithm are utilized to synthesize a new trajectory dataset for publication. Subsequently, a radix tree structure that satisfies differential privacy is defined. In comparison to the research method employing a prefix tree, the radix tree not only captures the spatiotemporal characteristics of the trajectories but also reduces space consumption. Finally, a novel method of noise addition is proposed. In contrast to the traditional layer-by-layer noise addition approach, our method reduces the cost of noise addition and enhances data availability. Experimental results demonstrate that TPRT exhibits superior data availability compared to the baseline methods.

Asymptotic behavior for Kirchhoff type stochastic plate equations on unbounded domains

This paper is concerned with the asymptotic behaviour of solutions to a class of Kirchhoff type stochastic nonlinear plate equations with dispersive and viscosity dissipative terms driven additive noise defined on the entire space Rn. The existence, uniqueness as well as upper semi-continuity of pullback random attractors are proved in H2(Rn)×H1(Rn).

Efficient approximation of stochastic turning process based on power spectral density

Turning is one of the most important material removal processes in manufacturing, where the proper understanding of the process is crucial for the quality of the final product. In this study, the stochastic cutting force is utilized to enhance the existing 1-degree-of-freedom turning model. A stochastic model is adopted to address the stochastic resonance phenomenon occurring near stability boundaries. Additionally, a novel simplified stochastic model is introduced with additive noise only. The comparison of the two models reveals that, with the recommended noise intensity of 0.1 to 1%, there is no significant difference in the stability charts and mean square characteristics between the two models. As a result, the time-consuming numerical methods can be bypassed, as the simplified model offers a computationally more efficient analytical approach to compute variance based on power spectral density (PSD). By combining techniques such as D-separation to determine stability boundaries and the PSD-based variance calculation, it only takes a minute instead of hours to construct a heatmap using the introduced simplified stochastic turning model that clearly outlines dangerous stochastic resonance regions inside the stable domain.

An efficient method for solving high-dimension stationary FPK equation of strongly nonlinear systems under additive and/or multiplicative white noise

Engineering structures may suffer from drastic nonlinear random vibrations in harsh environments. Random vibration has been extensively studied since 1960s, but is still an open problem for large-scale strongly nonlinear systems. In this paper, a random vibration analysis method based on the Neural Networks for large-scale strongly nonlinear systems under additive and/or multiplicative Gaussian white noise (GWN) excitations is proposed. In the proposed method, the high-dimensional steady-state Fokker–Planck-Kolmogorov (FPK) equation governing the state’s probability density function (PDF) is firstly reduced to low-dimensional FPK equation involving only the interested state variables, generally one or two dimensions. The equivalent drift coefficients (EDCs) and diffusion coefficients (EDFs) in the low-dimensional FPK equation are proven to be the conditional mean of the coefficients given the interested variables. Furthermore, it is shown that the conditional mean can be optimally estimated by regression. Subsequently, the EDCs and EDFs, as functions of the retained variables, are approximated by the semi-analytical Radial Basis Functions Neural Networks trained with samples generated by a few deterministic analyses. Finally, the Physics Informed Neural Network is employed to solve the reduced steady-state FPK equation, and the PDF of the system responses is obtained. Four typical examples under additive and/or multiplicative GWN excitations are used to examine the accuracy and efficiency of the proposed method by comparing its results with the exact solution (if available) or Monte Carlo simulations. The proposed method also exhibits greater accuracy than the globally-evolving-based generalized density evolution equation scheme, a similar method of its kind, especially for strongly nonlinear systems. Notably, even though steady-state systems are applied in this paper, there is no obstacle to extending the proposed framework to transient systems.

High-bandwidth low-current measurement system for automated and scalable probing of tunnel junctions in liquids.

Tunnel junctions have long been used to immobilize and study the electronic transport properties of single molecules. The sensitivity of tunneling currents to entities in the tunneling gap has generated interest in developing electronic biosensors with single molecule resolution. Tunnel junctions can, for example, be used for sensing bound or unbound DNA, RNA, amino acids, and proteins in liquids. However, manufacturing technologies for on-chip integrated arrays of tunnel junction sensors are still in their infancy, and scalable measurement strategies that allow the measurement of large numbers of tunneling junctions are required to facilitate progress. Here, we describe an experimental setup to perform scalable, high-bandwidth (>10kHz) measurements of low currents (pA-nA) in arrays of on-chip integrated tunnel junctions immersed in various liquid media. Leveraging a commercially available compact 100kHz bandwidth low-current measurement instrument, we developed a custom two-terminal probe on which the amplifier is directly mounted to decrease parasitic probe capacitances to sub-pF levels. We also integrated a motorized three-axis stage, which could be powered down using software control, inside the Faraday cage of the setup. This enabled automated data acquisition on arrays of tunnel junctions without worsening the noise floor despite being inside the Faraday cage. A deliberately positioned air gap in the fluidic path ensured liquid perfusion to the chip from outside the Faraday cage without coupling in additional noise. We demonstrate the performance of our setup using rapid current switching observed in electromigrated gold tunnel junctions immersed in deionized water.

Robust Tensor Completion via Capped Frobenius Norm.

Tensor completion (TC) refers to restoring the missing entries in a given tensor by making use of the low-rank structure. Most existing algorithms have excellent performance in Gaussian noise or impulsive noise scenarios. Generally speaking, the Frobenius-norm-based methods achieve excellent performance in additive Gaussian noise, while their recovery severely degrades in impulsive noise. Although the algorithms using the lp -norm ( ) or its variants can attain high restoration accuracy in the presence of gross errors, they are inferior to the Frobenius-norm-based methods when the noise is Gaussian-distributed. Therefore, an approach that is able to perform well in both Gaussian noise and impulsive noise is desired. In this work, we use a capped Frobenius norm to restrain outliers, which corresponds to a form of the truncated least-squares loss function. The upper bound of our capped Frobenius norm is automatically updated using normalized median absolute deviation during iterations. Therefore, it achieves better performance than the lp -norm with outlier-contaminated observations and attains comparable accuracy to the Frobenius norm without tuning parameter in Gaussian noise. We then adopt the half-quadratic theory to convert the nonconvex problem into a tractable multivariable problem, that is, convex optimization with respect to (w.r.t.) each individual variable. To address the resultant task, we exploit the proximal block coordinate descent (PBCD) method and then establish the convergence of the suggested algorithm. Specifically, the objective function value is guaranteed to be convergent while the variable sequence has a subsequence converging to a critical point. Experimental results based on real-world images and videos exhibit the superiority of the devised approach over several state-of-the-art algorithms in terms of recovery performance. MATLAB code is available at https://github.com/Li-X-P/Code-of-Robust-Tensor-Completion.

A full-scale complementary dynamic comparator

Abstract This paper presents a dynamic comparator that achieves precise comparison across the entire full-scale range. The comparator, an essential component module in analog-to-digital converters (ADCs), is influenced by its input signal range, speed, and offset voltage, all of which impact the ADC’s performance. In the proposed comparator, a pre-amplification stage using PMOS as the input is incorporated alongside the comparator utilizing NMOS as the input, creating a complementary structure. This design ensures that at least one pre-amplification stage operates effectively, thereby maintaining the accuracy of the comparator as the input signal varies across the entire full-scale voltage range (0 to VDD). Through sound circuit design, the proposed comparator effectively avoids introducing additional distortion and noise. The performance of the comparator is verified under the 180 nm process. The comparator achieves accurate comparison across the entire full-scale range, with a standard deviation σ of the input offset voltage of 6 mV, noise of 450 uV, and a layout area of 467.36 um2. Simulation results demonstrate that the comparator exhibits excellent performance, providing stability assurance for the ADC and extending the ADC’s input signal range.

Transformer neural networks for closed-loop adaptive optics using nonmodulated pyramid wavefront sensors

Context. The pyramid wavefront sensor (PyWFS) provides the required sensitivity for demanding future adaptive optics (AO) instruments. However, the PyWFS is highly nonlinear and requires the use of beam modulation to successfully close an AO loop under varying atmospheric turbulence conditions. This comes at the expense of a loss in sensitivity. Aims. We trained, analyzed, and compared the use of deep neural networks (NNs) as nonlinear estimators for the nonmodulated PyWFS, identifying the most suitable NN architecture for a reliable closed-loop AO. Methods. We developed a novel training strategy for NNs that seeks to accommodate for changes in residual statistics between open and closed loops, plus the addition of noise for robustness purposes. Through simulations, we tested and compared several deep NNs from classical to new convolutional neural networks (CNNs), plus the most recent transformer neural network (TNN; global context visual transformer, GCViT), first for an open loop and then for a closed loop. By identifying and properly retraining the most adequate deep neural net, we tested its simulated performance first in an open loop and then for closing an AO loop at a variety of noise and turbulence conditions. We finally tested the trained NN ability to close a real AO loop for an optical bench. Results. Using open-loop simulated data, we observe that a TNN (GCViT) largely surpasses any CNN in estimation accuracy in a wide range of turbulence conditions. Moreover, the TNN performs better in a simulated closed loop than CNNs, avoiding estimation issues at the pupil borders. When closing the loop at strong turbulence and low noise, the TNN using nonmodulated PyWFS data is able to close the loop, similar to a PyWFS with 12λ/D of modulation. When the noise is increased, only the TNN is able to close the loop, while the standard linear reconstructor fails even when a modulation is introduced. Using the GCViT, we closed a real AO loop in the optical bench and achieved a Strehl ratio between 0.28 and 0.77 for turbulence conditions corresponding to Fried parameters ranging from 6 to 20 cm, respectively. Conclusions. Through a variety of simulated and experimental results, we demonstrate that a TNN is the most suitable architecture for extending the dynamic range without sacrificing sensitivity for a nonmodulated PyWFS. It opens the path for using nonmodulated Pyramid WFSs in an unprecedented range of atmospheric and noise conditions.

Accounting for observation noise in equation‐free forecasting: The hidden‐Markov S‐map

Abstract Ecosystems contain numerous species interacting with each other and the environment. However, data on all relevant state variables is rarely available, hampering inference and prediction. Empirical dynamic modelling (EDM) is a valuable tool for prediction, inference and control in such partially observed systems. However, EDM typically assumes that the available time series are observed without error. Failing to account for observation noise strongly biases estimates of Lyapunov exponents and reduces forecast accuracy. To address this limitation, we propose incorporating EDM into a hidden Markov framework and using an iterative scheme based on the expectation maximization (EM) algorithm to obtain filtered state and parameter estimates. We evaluate the performance of this approach on several simulated dynamical systems with a range of additive noise levels, as well as on insect population time series. Accounting for observation noise improved accuracy of population forecasts and estimates of Lyapunov exponents (LE) over a wide range of noise levels relevant to ecological time series.

Smart Recognition and Authentication based on Haar Cascade Classifier and Visual Cryptography

The algorithm with an E-verification method is proposed that combines automated facial recognition technology with digital media and later it combines aspects of secret data exchange and visual cryptography. A face detection technique based on Internet of Things (IoT) selects features using the Principal Component Analysis (PCA) algorithm and the Haar cascade classifier. The selected face serving as a cover follows two level Discrete Haar Wavelet Transform. The shares generated from digital signature and fingerprint are diffused into the converted coefficients. Furthermore, the imperceptibility of the additional noise is increased by a bit-level noise reduction technique. Authenticity is confirmed by regenerating a message digest at the receiving end, and the extraction process operates in complete blindness. The approach is suitable for smart card design and may be used as an automatic recognition system in a real-world setting. Performance comparisons show a notable improvement over other approaches that are comparable. Additionally, the technique is effective against some related attacks.

Self-gating stochastic-resonance-based autoencoder for unsupervised learning.

Incorporating additive noise components to an ensemble of McCulloch-Pitts neurons can enhance the information representation of the input, asymptotically approaching the average firing probability for large enough ensembles. We further multiply the input by the average firing probability to control the higher probability of self-gating, thereby forming a unified noise-boosted activation model with learnable noise-related hyperparameters. This gating strategy plays a crucial role in improving the performance of neural networks, as evidenced by the optimization of the autoencoder loss at nonzero optimal-noise-scaling hyperparameters, a phenomenon termed self-gating stochastic resonance. Experiments with designed autoencoders using noise-boosted activation functions demonstrate the potential applications of the self-gating stochastic resonance effect in the field of unsupervised learning.

A deep‐learning framework for enhancing habitat identification based on species composition

AbstractAimsThe accurate classification of habitats is essential for effective biodiversity conservation. The goal of this study was to harness the potential of deep learning to advance habitat identification in Europe. We aimed to develop and evaluate models capable of assigning vegetation‐plot records to the habitats of the European Nature Information System (EUNIS), a widely used reference framework for European habitat types.LocationThe framework was designed for use in Europe and adjacent areas (e.g., Anatolia, Caucasus).MethodsWe leveraged deep‐learning techniques, such as transformers (i.e., models with attention components able to learn contextual relations between categorical and numerical features) that we trained using spatial k‐fold cross‐validation (CV) on vegetation plots sourced from the European Vegetation Archive (EVA), to show that they have great potential for classifying vegetation‐plot records. We tested different network architectures, feature encodings, hyperparameter tuning and noise addition strategies to identify the optimal model. We used an independent test set from the National Plant Monitoring Scheme (NPMS) to evaluate its performance and compare its results against the traditional expert systems.ResultsExploration of the use of deep learning applied to species composition and plot‐location criteria for habitat classification led to the development of a framework containing a wide range of models. Our selected algorithm, applied to European habitat types, significantly improved habitat classification accuracy, achieving a more than twofold improvement compared to the previous state‐of‐the‐art (SOTA) method on an external data set, clearly outperforming expert systems. The framework is shared and maintained through a GitHub repository.ConclusionsOur results demonstrate the potential benefits of the adoption of deep learning for improving the accuracy of vegetation classification. They highlight the importance of incorporating advanced technologies into habitat monitoring. These algorithms have shown to be better suited for habitat type prediction than expert systems. They push the accuracy score on a database containing hundreds of thousands of standardized presence/absence European surveys to 88.74%, as assessed by expert judgment. Finally, our results showcase that species dominance is a strong marker of ecosystems and that the exact cover abundance of the flora is not required to train neural networks with predictive performances. The framework we developed can be used by researchers and practitioners to accurately classify habitats.

Privacy-preserving method for sensitive partitions of electricity consumption data based on hybrid differential privacy and k-anonymity

Abstract With the development of smart grid, traditional privacy protection methods are no longer sufficient to cope with the mining and analysing of users’ electricity consumption data, which can easily lead to the leakage of users’ privacy. In this paper, for the challenge of privacy protection of user electricity data in smart grid, we propose a privacy protection method for sensitive partition of electricity data based on hybrid differential privacy and k-anonymity technique, which identifies pattern-specific quasi-identifiers by random forest technique and divides the data into privacy-invasive and non-privacy-invasive partitions, and adopts the Laplacian noise addition (numerical quasi-identifiers) and data generalisation (sub-types of quasi-identifiers) techniques to achieve differential privacy protection for different partitions. Finally, it is experimentally verified that the method performs better in terms of information reduction accuracy and execution time, effectively striking a balance between protecting user privacy and maintaining data utility.

Fast bicriteria streaming algorithms for submodular cover problem under noise models

The Submodular Cover (SC) problem has attracted the attention of researchers because of its wide variety of applications in many domains. Previous studies on this problem have focused on solving it under the assumption of a non-noise environment or using the greedy algorithm to solve it under noise. However, in some applications, the data is often large-scale and brings a noisy version, so the existing solutions are ineffective or not applicable to large and noisy data. Motivated by this phenomenon, we study the Submodular Cover under Noises (SCN) problem and propose two efficient streaming algorithms, which provide a solution with theoretical bounds under two common noise models, multiplicative and additive noises. The experimental results indicate that our proposed algorithms not only provide the solution with a high objective function value but also outperform the state-of-the-art algorithm in terms of both the number of queries and the running time.

White dwarf constraints on geological processes at the population level

ABSTRACT White dwarf atmospheres are frequently polluted by material from their own planetary systems. Absorption features from Ca, Mg, Fe, and other elements can provide unique insights into the provenance of this exoplanetary material, with their relative abundances being used to infer accretion of material with core- or mantle-like composition. Across the population of white dwarfs, the distribution of compositions reveals the prevalence of geological and collisional processing across exoplanetary systems. By predicting the distribution of compositions in three evolutionary scenarios, this work assesses whether they can explain current observations. We consider evolution in an asteroid belt analogue, in which collisions between planetary bodies that formed an iron core lead to core- or mantle-rich fragments. We also consider layer-by-layer accretion of individual bodies, such that the apparent composition of atmospheric pollution changes during the accretion of a single body. Finally, we consider that compositional spread is due to random noise. We find that the distribution of Ca, Fe, and Mg in a sample of 202 cool DZs is consistent with the random noise scenario, although 7 individual systems show strong evidence of core-mantle differentiation from additional elements and/or low noise levels. Future surveys that detect multiple elements in each of a few hundred white dwarfs, with well-understood biases, have the potential to confidently distinguish between the three models.

Stochastic modulation of the Montgomery’s rings to generate the self-imaging effect with revival features

The synthesis of optical fields that follows a stochastic process and whose statistical mean values generate the self-imaging-revivals effect is analyzed. A sufficient condition for optical fields to exhibit the self-imaging effect occurs when the frequency representation is located on the Montgomery’s rings. The study is performed by implementing stationary random fluctuations on the Montgomery’s rings of additive and multiplicative types. The additive noise is of the stochastic radial walk type with zero mean. Multiplicative noise generates stochastic angular fluctuations in the rings and is implemented using the Karhunen–Loève theorem. The modal representation implicit in the theorem is obtained by interpreting the self-imaging planes as an optical cavity, assuring the statistical periodicity of the noise. A time consonance of the random fluctuations for each ring allows to determine the revivals period for the self-imaging optical fields. The model is corroborated by computer simulations.

Approximate averaged derivative moments and stochastic response of high-DOF quasi-non-integrable Hamiltonian systems under Poisson white noises

Stochastic response prediction is one of the principal topics in diverse branches of engineering, such as aerospace engineering, mechanical engineering, and vehicle engineering. However, the challenge of addressing high-dimensional partial differential equations or evaluating high-dimensional domain integrals in determining averaged derivative moments has limited the research. This study proposes a method to predict the stochastic response of high-degree-of-freedom (DOF) quasi-non-integrable Hamiltonian systems under Poisson white noises. The original finite DOF system is reduced to a one-dimensional one governing the Hamiltonian by applying the stochastic averaging method, and the associated reduced generalized Fokker–Planck–Kolmogorov (GFPK) equation is derived. Then, the two-step generalized elliptical coordinate transformation is extended to evaluate averaged derivative moments that are the key to obtaining the stationary probability density function (SPDF) for probabilistic information prediction. Moreover, the perturbation method is introduced to address the high-order GFPK equation. Finally, an 8-DOF strongly nonlinear system under purely additive Poisson white noises is given as an example to highlight the accuracy of the proposed method. Results from the proposed method show good agreement with those from Monte Carlo simulations, which indicates that the proposed method can be applied to assess the response of high-DOF quasi-non-integrable Hamiltonian systems under Poisson white noises. In addition, if the potential energy of an arbitrary finite n-DOF system is the same form as that in Appendix B, pertinent high-dimensional domain integrals are converted into explicit expressions when n is even.