Levels Of Random Noise Research Articles

Detection of Underground Anomalies Using Analysis of Ground Penetrating Radar Attribute

Need of specifying underground construction works for supporting further tasks as maintenance, repairing, or setting up new underground structures. For these needs, ground penetrating radar, one of the efficient geophysical methods, can bring high-resolution and quick underground image revealing existence of both natural and artificial anomalies. Its fixed receiver-transmitter antennas setting as constant offset is commonly used in urban areas. Conventionally, hyperbolae events are crucial indicator for scattering objects as kinds of pipes, water drainage system, and concrete building structures as well as sink holes. Calculation of their depths and sizes requires migration analysis with the environment velocity. Migrated sections with different velocity show different chaos degrees of transformation from a hyperbola diffraction curve to its focused area. We have researched diagrams of different Ground Penetrating Radar attributes as energy, entropy, and varimax dependent on two variables, velocity and window zone covering diffraction events from a set of synthetic data and real data, in specifying the environment velocity. We have developed a novel technique for evaluation of the ground velocity and object’s size by combination of the new varimax diagram and the Kirchhoff migration method. The technique can define contribution of diffracted ground penetrating radar waves for building the diagram after removing the reflection contribution. The synthetic datasets consist of different random background noise levels and expressions of different-sized circular and rectangular pipes. The real data is measured for detecting two underground gas pipes in Ba Ria – Vung Tau province, Vietnam.

Improvement of Neural Networks Applied to Photoacoustic Signals of Semiconductors with Added Noise

This paper provides an overview of the characteristics of different neural networks trained on the same theoretical database of n-type silicon photoacoustic signals. By adding different levels of random Gaussian noise to the training input signals, two important goals were achieved. First, the optimal level of noise was found which significantly shortens the training networks with minimal loss of accuracy of its predictions. Second, the termination criteria of networks training were activated to avoid overtraining, i.e., networks generalization was performed. A networks efficiency analysis was performed on both theoretical and experimental photoacoustic signals, resulting in a selection of one neural network that is optimal to the performance requirements of the real experiment. It is indicated that the application of such trained networks is more reliable on thicker semiconductors, whose thickness is greater than the value of the carrier diffusion length in the investigated sample.

Identification of White Matter Networks Engaged in Object (Face) Recognition Showing Differential Responses to Modulated Stimulus Strength.

Blood-oxygenation-level-dependent (BOLD) signals in magnetic resonance imaging indirectly reflect neural activity in cortex, but they are also detectable in white matter (WM). BOLD signals in WM exhibit strong correlations with those in gray matter (GM) in a resting state, but their interpretation and relationship to GM activity in a task are unclear. We performed a parametric visual object recognition task designed to modulate the BOLD signal response in GM regions engaged in higher order visual processing, and measured corresponding changes in specific WM tracts. Human faces embedded in different levels of random noise have previously been shown to produce graded changes in BOLD activation in for example, the fusiform gyrus, as well as in electrophysiological (N170) evoked potentials. The magnitudes of BOLD responses in both GM regions and selected WM tracts varied monotonically with the stimulus strength (noise level). In addition, the magnitudes and temporal profiles of signals in GM and WM regions involved in the task coupled strongly across different task parameters. These findings reveal the network of WM tracts engaged in object (face) recognition and confirm that WM BOLD signals may be directly affected by neural activity in GM regions to which they connect.

Minerals and ore deposits exploration using meta-heuristic based optimization on magnetic data

The difficulties in unravelling the tectonic structures, in some cases, prevent the understanding of the ore bodies' geometry, leading to mistakes in mineral exploration, mine planning, evaluation of ore deposits, and even mineral exploitation. For that reason, many geophysical techniques are introduced to reveal the type, dimension, and geometry of these structures. Among them, electric methods, self-potential, electromagnetic, magnetic and gravity methods. Global meta-heuristic technique using Whale Optimization Algorithm (WOA) has been utilized for assessing model parameters from magnetic anomalies due to a thin dike, a dipping dike, and a vertical fault like/shear zone geological structure. These structures are commonly associated with mineralization. This modern algorithm was firstly applied on a free-noise synthetic data and to a noisy data with three different levels of random noise to simulate natural and artificial anomaly disturbances. Good results obtained through the inversion of such synthetic examples prove the validity and applicability of our algorithm. Thereafter, the method is applied to real case studies taken from different ore mineralization resembling different geologic conditions. Data are taken from Canada, United States, Sweden, Peru, India, and Australia. The obtained results revealed good correlation with previous interpretations of these real field examples.

Joint Minimization of the Mean and Information Entropy of the Matching Filter Distribution for a Robust Misfit Function in Full-Waveform Inversion

A full-waveform inversion (FWI) is a highly nonlinear inversion methodology. FWI tends to converge to a local minimum rather than a global one. We refer to this phenomenon as “cycle skipping” in FWI. A cost-effective solution for resolving this issue is to design a more convex misfit function for the optimization problem. A global comparison based on using a matching filter (MF) admits more robust misfit functions. In this case, we would compute an MF first by deconvolving the predicted data from the measured ones. When the velocity model is accurate, the predicted data resemble the measured ones, and the resulting MF would be an approximated Dirac delta function. If the velocity produces data that are different from the observed ones, a misfit function can be formulated by penalizing the energy away from the zero-lag time (the center). Here, we develop a general mechanism for an evolution of the MF to our objective in FWI. Specifically from the statistics point of view, rather than using a penalty, we propose a novel misfit by minimization of the mean and information entropy of the MF distribution. We show that the resulting misfit function can mitigate the “cycle skipping” as well as reduce the mean and variance of the resulting MF distribution. We use a modified Marmousi example to demonstrate the features of the proposed misfit. We also evaluate the robustness of the proposed method using inaccurate (rotation in phase) source wavelets and measured data with different levels of Gaussian random noise.

Fast and precise spatial-carrier phase-shifting algorithm with the matrix VU factorization

A fast and precise spatial-carrier phase-shifting algorithm based on the matrix VU factorization strategy that can realize dynamic real-time phase detection is proposed. First, the proposed algorithm divides the spatial-carrier interferogram into four phase-shifting subinterferograms. Second, the matrix VU factorization strategy, an excellent fast iterative algorithm, is used to accurately obtain the measured phase from these subinterferograms. Numerical simulation and experimental comparison verify that this method is an efficient and accurate single-frame phase demodulation algorithm. Meanwhile, the performance of the proposed method is analyzed and discussed for the influencing factors, such as random noise level, carrier-frequency value, and carrier-frequency direction. The results show that the method proposed is a fast and precise phase detection method that provides another effective solution for dynamic real-time phase measurement.

Age-Dependent Statistical Changes of Involuntary Head Motion Signatures Across Autism and Controls of the ABIDE Repository.

The DSM-5 definition of autism spectrum disorders includes sensory issues and part of the sensory information that the brain continuously receives comes from kinesthetic reafference, in the form of self-generated motions, including those that the nervous systems produce at rest. Some of the movements that we self-generate are deliberate, while some occur spontaneously, consequentially following those that we can control. Yet, some motions occur involuntarily, largely beneath our awareness. We do not know much about involuntary motions across development, but these motions typically manifest during resting state in fMRI studies. Here we ask in a large data set from the Autism Brain Imaging Exchange repository, whether the stochastic signatures of variability in the involuntary motions of the head typically shift with age. We further ask if those motions registered from individuals with autism show a significant departure from the normative data as we examine different age groups selected at random from cross-sections of the population. We find significant shifts in statistical features of typical levels of involuntary head motions for different age groups. Further, we find that in autism these changes also manifest in non-uniform ways, and that they significantly differ from their age-matched groups. The results suggest that the levels of random involuntary motor noise are elevated in autism across age groups. This calls for the use of different age-appropriate statistical models in research that involves dynamically changing signals self-generated by the nervous systems.

A Supervised Descent Learning Technique for Solving Directional Electromagnetic Logging-While-Drilling Inverse Problems

In this article, a new scheme based on the supervised descent method (SDM) for solving directional electromagnetic logging-while-drilling (LWD) inverse problems is proposed. The SDM provides us a new perspective to combine the classical gradient-based inversion and machine-learning-based inversion schemes. It iteratively learns a set of descent directions in the offline training process, where the training model set is generated in advance according to the prior information, and then updates the models with the learned descent directions as well as data residuals in the prediction stage, resulting in great flexibility to incorporate prior information, the capability of skipping local minima, and accelerated convergence. The generalization ability of the SDM to interrogate new models that are not contained in the training model set is also explored. By utilizing real-time information obtained from the logging process, the learned descent directions can be slightly revised with a higher efficiency to get closer to the true model. In addition, we probe the sensitivity of the SDM by adding different levels of random noise to the measurements. Numerical examples demonstrate that SDM-based inversion can achieve a higher resolution, faster convergence, and higher robustness than conventional schemes such as Occam’s inversion.

A QSC method for fractional subdiffusion equations with fractional boundary conditions and its application in parameters identification

A quadratic spline collocation (QSC) method combined with L1 time discretization, named QSC-L1, is proposed to solve fractional subdiffusion equations with artificial boundary conditions. A novel norm-based stability and convergence analysis is carefully discussed, which shows that the QSC-L1 method is unconditionally stable in a discrete space–time norm, and has a convergence order O(τ2−α+h2), where τ and h are the temporal and spatial step sizes, respectively. Then, based on fast evaluation of the Caputo fractional derivative (see, Jiang et al., 2017), a fast version of QSC-L1 which is called QSC-FL1 is proposed to improve the computational efficiency. Two numerical examples are provided to support the theoretical results. Furthermore, an inverse problem is considered, in which some parameters of the fractional subdiffusion equations need to be identified. A Levenberg–Marquardt (L–M) method equipped with the QSC-FL1 method is developed for solving the inverse problem. Numerical tests show the effectiveness of the method even for the case that the observation data is contaminated by some levels of random noise.

Point spread function modelling for wide-field small-aperture telescopes with a denoising autoencoder

ABSTRACTThe point spread function reflects the state of an optical telescope and it is important for the design of data post-processing methods. For wide-field small-aperture telescopes, the point spread function is hard to model because it is affected by many different effects and has strong temporal and spatial variations. In this paper, we propose the use of a denoising autoencoder, a type of deep neural network, to model the point spread function of wide-field small-aperture telescopes. The denoising autoencoder is a point spread function modelling method, based on pure data, which uses calibration data from real observations or numerical simulated results as point spread function templates. According to real observation conditions, different levels of random noise or aberrations are added to point spread function templates, making them realizations of the point spread function (i.e. simulated star images). Then we train the denoising autoencoder with realizations and templates of the point spread function. After training, the denoising autoencoder learns the manifold space of the point spread function and it can map any star images obtained by wide-field small-aperture telescopes directly to its point spread function. This could be used to design data post-processing or optical system alignment methods.

THE MOBILE SYSTEM REDUCTION FOR THE VIBRATION CONTROL IMPLEMENTATION

Since the mining and oil and gas industries play a decisive role in the Ukrainian economy, the adequacy and proper assessment of the accuracy of the monitoring is of great national importance. A mathematical model for the measurement of MSCs is constructed, which determines the sequence of mathematical operations that must be performed to obtain the quantitative characteristics of the objects of control. If there is a function that is a solution and that describes the object of the MSC, then it is a reduction to the ideal MSC. The solution of the problem of reduction (synthesis) MSC is realized by the choice of design and is provided with such a connection between the signals at its input and output MSC, which leads to the best results. This formulation of the problem of reducing the MSC has several disadvantages. The MSC measurement result is always influenced by a number of minor factors. Their effect leads to the fact that the measured value of a certain value is different from the value predicted by the model of measurement of the ISC on the noise (experiment error), which is random. The noise level of MSCs has a significant effect on the result of mathematical processing, and the less the noise, the better the result of the reduction of MSCs. Previously, the task of instrumentation was to create an MSC that provides the least distortion of the measurement results, while using mathematical methods to reduce instrumentation the task of reducing instrumentation noise is MSC. The given solution is realized by the choice of design and is provided with such a connection between the input and output signals, which leads to a decrease in the level of random noise MSC. The description of MSC enhancement has the instability of the solution of the equation with respect to the initial data errors, which is a property of almost all integral equations and does not depend on the method of their solution. The proposed mathematical method of reduction of the mobile control system (MSC) as one of the variants of regularization of the incorrectly set problem arose and was further developed under the influence of the ideas of academician AN Tikhonov and Professor Yu.P. Pytiev . The author suggests taking a different look at the control tasks and the accuracy of assessing the accuracy of MCSs by reducing the level of random noise. The author proposed the implementation of the MCS by choosing a design and providing such a connection between the signal at its input and output, which leads to the best results in solving reduction problems. The author proposed an adaptable model of MCSs using modern ideas and mathematical methods.

Evaluating gravity gradient components based on a reweighted inversion method

In gravity gradient inversion, to choose an appropriate component combination is very important, that needs to understand the function of each component of gravity gradient in the inversion. In this paper, based on the previous research on the characteristics of gravity gradient components, we propose a reweighted inversion method to evaluate the influence of single gravity gradient component on the inversion resolution The proposed method only adopts the misfit function of the regularized equation and introduce a depth weighting function to overcome skin effect produced in gravity gradient inversion. A comparison between different inversion results was undertaken to verify the influence of the depth weighting function on the inversion result resolution. To avoid the premise of introducing prior information, we select the depth weighting function based on the sensitivity matrix. The inversion results using the single-prism model and the complex model show that the influence of different components on the resolution of inversion results is different in different directions, however, the inversion results based on two kind of models with adding different levels of random noise are basically consistent with the results of inversion without noises. Finally, the method was applied to real data from the Vinton salt dome, Louisiana, USA.

Multiple-linear regression to best-estimate of gravity parameters related to simple geometrical shaped structures

Abstract A new interpretative approach is proposed to best-estimate of gravity parameters related to simple geometrical shaped structures such as a semi-infinite vertical cylinder, an infinite horizontal cylinder, and a sphere like structures. The proposed technique is based on the multiple-linear regression oriented towards estimating the model parameters, e.g., the depth from the surface to the center of the buried structure (sphere or infinite horizontal cylinder) or the depth from the surface to the top of the buried object (semi-infinite vertical cylinder), the amplitude coefficient, and the horizontal location from residual gravity anomaly profile. The validity of the proposed approach is firstly demonstrated through testing different synthetic data set corrupted and contaminated by a white Gaussian random noise level. The theoretical synthetic obtained results obviously show that the estimated parameters values, derived by the proposed technique are close to the assumed true parameters values. This approach is applied on five real field residual gravity anomalies taken from Cuba, Sweden, Iran, USA, and Germany, where the efficacy of this new approach is consequently proven. A comparable and acceptable agreement is noticed between the results derived by this proposed approach and those obtained from the real field data information.

Working with Gaussian Random Noise for Multi-Sensor Archaeological Prospection: Fusion of Ground Penetrating Radar Depth Slices and Ground Spectral Signatures from 0.00 m to 0.60 m below Ground Surface

The integration of different remote sensing datasets acquired from optical and radar sensors can improve the overall performance and detection rate for mapping sub-surface archaeological remains. However, data fusion remains a challenge for archaeological prospection studies, since remotely sensed sensors have different instrument principles, operating in different wavelengths. Recent studies have demonstrated that some fusion modelling can be achieved under ideal measurement conditions (e.g., simultaneously measurements in no hazy days) using advance regression models, like those of the nonlinear Bayesian Neural Networks. This paper aims to go a step further and investigate the impact of noise in regression models, between datasets obtained from ground-penetrating radar (GPR) and portable field spectroradiometers. Initially, the GPR measurements provided three depth slices of 20 cm thickness, starting from 0.00 m up to 0.60 m below the ground surface while ground spectral signatures acquired from the spectroradiometer were processed to calculate 13 multispectral and 53 hyperspectral indices. Then, various levels of Gaussian random noise ranging from 0.1 to 0.5 of a normal distribution, with mean 0 and variance 1, were added at both GPR and spectral signatures datasets. Afterward, Bayesian Neural Network regression fitting was applied between the radar (GPR) versus the optical (spectral signatures) datasets. Different regression model strategies were implemented and presented in the paper. The overall results show that fusion with a noise level of up to 0.2 of the normal distribution does not dramatically drop the regression model between the radar and optical datasets (compared to the non-noisy data). Finally, anomalies appearing as strong reflectors in the GPR measurements, continue to provide an obvious contrast even with noisy regression modelling.

Influence of the error description on model-based design of experiments

Measurement noise and errors are inherent to all experimental measurements, thus it is necessary to consider them while optimally designing any experiment. The scope of this paper is to determine the influence of various error descriptions in the measurement data considering different approaches for the model-based design of experiments. The considered types of error are: random and systematic. The random error is assumed to be normally distributed wita finite variance. The systematic error is represented in two ways: either as a relative factor to the “exact” data or as a drift related to measurement time. Combinations of these types of error form the used error descriptions. Basically, two methods of finding the optimal experimental design are used: one is based on the Fisher Information Matrix (FIM) and the other one is using mean-squared reconstruction errors (MSE). Based on an application example which is a cantilever beam, a slender civil structure, consisting of two different materials, implemented by the Young’s modulus, the optimal designs for three sensor locations are calculated for 28 different error combinations which differ in error type and noise level. The results for the best sensor setups are displayed and discussed depending on the method used for the design of the experiment and the error description.The evaluation of the two approaches shows that the FIM does not take systematic errors into account and also it is not depending on the random noise level, whereas the MSE approach is considering systematic errors, but to its disadvantage, it is computationally much more costly.

Correcting airborne gravity data for overburden thickness: a case study from the Nechako interior plateau, British Columbia

Large areas of bedrock in Canada, such as in the interior plateau of British Columbia, are covered by a thick glacial overburden. Lateral variations in overburden thickness can create spurious anomalies in gravity data. These anomalies can be of a size and amplitude similar to those associated with mineral bodies and can be mistaken for them. A methodology is introduced that corrects gravity data for changes in overburden thickness through the use of a bedrock topography map created by integrating information from a helicopter transient electromagnetic survey with geological survey data, well water data, and gravel pit locations. The approach is tested for a 68 km × 38 km area in the prospective Nechako interior plateau of British Columbia, Canada. The methodology extends the traditional Bouguer corrections by taking into account the gravitational contribution of the overburden. Results show that the capability of an airborne survey to detect a change in overburden thickness depends primarily on survey line spacing and to a lesser extent on the level of random noise in the gravity data. The bedrock topography correction has the capability of removing the gravitational attraction of overburden for the purpose of revealing, through interpretation, geological structures in the gravity data that originate from the bedrock and are otherwise concealed.

Contribution of random noise in the ITER RNC diamond neutron detectors pulses to the counting rate uncertainty

The main goal of the ITER Radial Neutron Camera (RNC) is to provide the plasma neutron emission profile (neutron emissivity) through measurement of the uncollided 14 MeV and 2.5 MeV neutrons from deuterium-tritium (DT) and deuterium-deuterium (DD) fusion reactions. The system is based on an array of detectors (diamonds are among the candidate detectors) located in collimated lines of sight (LOS) viewing the plasma through the ITER Equatorial Port Plug #1. Tomographic reconstruction techniques are used to calculate the neutron emissivity.The contribution of random noise on diamond detector pulses to the count rate uncertainty is investigated in this paper. The energy spectrum of the neutrons impinging on the detector has been calculated by means of MCNP calculations for one line of sight of the RNC In-Port system. The spectrum has been convoluted with the diamond detector response functions and the Pulse Height Spectrum (PHS) has been obtained. Experiments have been carried out with the CAEN™ 5810D detector emulator, that is able to produce arbitrary pulse height distributions as those expected in the ITER RNC. Random noise has been added on each detector pulse of the distribution using the detector emulator. The resulting uncertainty produced on the count rate has been evaluated as a function of the random noise level.

Application of Multivariate Empirical Mode Decomposition to Noise Reduction in Seismic Signal

The three-component signals of earthquake waves are very complex, requiring filtering methods that can filter three-component signal simultaneously. A good seismic signal is a signal that is free of noise, both in the instrument noise and in the field noise. In this paper, an effective and efficient filter method is proposed to reduce noise on the three-component seismic signal, The proposed method use multivariate empirical mode decomposition (MEMD) to decompose a multivariate signal into several intrinsic mode functions (IMF). MEMD is highly adaptive and can be very satisfying in time-frequency characteristics of signals. The method requires no prior knowledge of the target signals. MEMD method was tested on synthetic data with the different random noise level. The result shows that this method can reduce the seismogram of signal noise efficiently. This method is very effective to reduce noise, both on synthetic and field data.

Attribute analysis improvement by means of smart averaging

Abstract Seismic attribute maps can benefit from dedicated processing for suppression of noise and improvement in geological feature delineation. Traditional 2D windowed frequency filtering, or smoothing, can degrade the required resolution and hence impacts interpretability. We propose a ‘Smart Averaging’ (SA) technique, which is an optimization routine based on specific criteria, and we show that the root mean square (RMS) deviation minimization criterion is effective for both spikes and random noise, providing both visual and interpretation improvement. It out-performs conventional fixed window smoothing, or averaging. The dependency between interpretation reliability, data resolution and random noise level is demonstrated. When the attribute maps have very high levels of noise, we show that interpretation is still successful, even if the attribute map detail is noticeably compromised.

Random Noise Suppression of Magnetic Resonance Sounding Oscillating Signal by Combining Empirical Mode Decomposition and Time-Frequency Peak Filtering

Magnetic resonance sounding (MRS) signals are always corrupted by random noise. Although time-frequency peak filtering (TFPF) has been proven to be an effective method to suppress the random noise, it shows shortcomings when processing the oscillating high-frequency MRS signal at about 2 kHz. In this study, a new method combining empirical mode decomposition (EMD) and TFPF is proposed to overcome the TFPF limitation when processing the MRS oscillating signal. With the help of EMD decomposition characteristics, the random-noise-corrupted MRS oscillating signal is first decomposed into several different components which contain frequencies ranging from the highest to the lowest ones. Then, the components which do not have signal frequency are discarded to bring down the level of random noise. The residual components are further processed by TFPF, respectively, based on the theory of instantaneous frequency estimation and the property of noise accumulation. Finally, the de-noised result is obtained by reconstructing the processed components. The numerical simulations on synthetic signals embedded in both artificial noise and real noise show the combined method can improve the signal-to-noise ratios and reduce the uncertainties of signal parameters. In addition, the combined method is applied following a standard processing scheme in field data, and better results are also obtained.