Denoising of aeromagnetic data via the wavelet transform

Geophysics ◽  
2001 ◽  
Vol 66 (6) ◽  
pp. 1793-1804 ◽  
Author(s):  
George E. Leblanc ◽  
William A. Morris
Keyword(s):  
Wavelet Transform ◽  
High Frequency ◽  
Random Noise ◽  
Synthetic Data ◽  
Analysis Procedure ◽  
Data Sets ◽  
Aeromagnetic Data ◽  
Wavelet Method ◽  
Southern Alberta ◽  
Geologic Data

Noise has traditionally been suppressed or eliminated in aeromagnetic data sets by the use of Fourier analysis filters and, to a lesser degree, nonlinear statistical filters. Although these methods are quite useful under specific conditions, they produce undesirable effects when denoising features of moderate to large amplitude and spatial extent. In this study, a new wavelet analysis procedure is presented that substantially reduces the contribution from high‐frequency random noise and noise that is user defined. Applications to both synthetic data and aeromagnetic data from southern Alberta, Canada, show that the wavelet method eliminates the noise portion of the signal more efficiently and retains a greater amount of geologic data than other methods.

Reducing the dependence of the analytic signal amplitude of aeromagnetic data on the source vector direction

Geophysics ◽  
2014 ◽  
Vol 79 (4) ◽  
pp. J55-J60 ◽  
Author(s):  
Gordon R. J. Cooper
Keyword(s):  
Synthetic Data ◽  
Magnetization Vector ◽  
Signal Amplitude ◽  
Analytic Signal ◽  
Data Sets ◽  
Aeromagnetic Data ◽  
3D Data ◽  
Vector Direction ◽  
2D Data ◽  
Derivatives Of

The analytic signal amplitude (As) is commonly used as an edge-detection filter for aeromagnetic data. For profile (2D) data, its shape is independent of the source magnetization vector direction, but this is not the case for map (3D) data. A modified analytic signal amplitude ([Formula: see text]) is introduced here which has a much reduced dependence on this vector for both contact and dike models. When the modified analytic signal amplitude was applied to synthetic data sets, it was more effective in enhancing the edges of the bodies than the standard As. Because it uses second-order derivatives of the magnetic field, the method is sensitive to noise and so an additional formulation was developed for noisy data sets that only use first-order derivatives.

scholarly journals Resolution Enhancement of GPR Data Using Bayesian Filtering Optimized by Machine Learning Algorithms

2020 ◽  
Author(s):  
Alireza HAJIAN ◽  
Rohollah Kimiaefar
Keyword(s):  
Fuzzy Inference ◽  
Random Noise ◽  
Resolution Enhancement ◽  
Synthetic Data ◽  
Real Data ◽  
Machine Learning Algorithms ◽  
Environmental Study ◽  
Data Sets ◽  
Bayesian Filtering ◽  
Inference System

Abstract Blurring coherence events is the result of applying many spatial and temporal filtering algorithmswhen they are applied in order to suppress background random noise. Bayesian Filtering (BF) also suffers from mentioned problem. This paper develops a method for optimizing BF by Adaptive Neuro-Fuzzy Inference System (ANFIS) and Fuzzy C-Mean (FCM)clustering. First the structure of the GPR image is extracted using FCM. The structure and output of the BF for a random part of the data are used to produce output values for training ANFIS and after that, by generalizing the trained network to all data, filtered data would be achieved. The proposed method is applied on synthetic data-sets as well as tworeal 2-D GPR images gathered in an environmental study project. Performance of the method is evaluated by comparing the results of the proposed method to the output of BF. In synthetic data, the SNR value improved 63 percent more than of BF’s outputandthe visual comparison of the results are suggesting better performance in noise cancellation and resolution enhancement, both in synthetic and real data-sets.

A 2D multistage median filter to reduce random seismic noise

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. V105-V110 ◽  
Author(s):  
Cai Liu ◽  
Yang Liu ◽  
Baojun Yang ◽  
Dian Wang ◽  
Jianguo Sun
Keyword(s):  
Seismic Data ◽  
High Frequency ◽  
Median Filter ◽  
Random Noise ◽  
Synthetic Data ◽  
Window Size ◽  
Median Filters ◽  
A Value ◽  
Final Data ◽  
Static Corrections

Random noise lowers the S/N of seismic data and decreases the accuracy of dynamic and static corrections, thus degrading final data quality. A 2D multistage median filter (MLM) that effectively reduces the high-frequency random noise can be implemented by applying 1D median filters (MF) in several directions and choosing a value derived from them to output at the center of the 2D window. The choice of window size depends on the intensity of the random noise and the percentage of the input data samples within the window that contain noise. Synthetic data can be used to demonstrate how to choose the window size. The tendency of the method to damage the signal while reducing the noise can be minimized by optimizing window size and by applying two passes with modest-sized windows as opposed to a single pass with a larger window. Results of using the method on prestack and poststack data from the Songliao basin in China demonstrate that the method is effective at both stages.

scholarly journals Electrophysiological aftereffects of high-frequency transcranial random noise stimulation (hf-tRNS): an EEG investigation

2021 ◽  
Author(s):  
Filippo Ghin ◽  
Louise O’Hare ◽  
Andrea Pavan
Keyword(s):  
High Frequency ◽  
Discrimination Task ◽  
Temporal Dynamics ◽  
Random Noise ◽  
Decomposition Analysis ◽  
Oscillatory Activity ◽  
Motion Direction ◽  
Time Frequency ◽  
Direction Discrimination ◽  
Transcranial Random Noise Stimulation

AbstractThere is evidence that high-frequency transcranial random noise stimulation (hf-tRNS) is effective in improving behavioural performance in several visual tasks. However, so far there has been limited research into the spatial and temporal characteristics of hf-tRNS-induced facilitatory effects. In the present study, electroencephalogram (EEG) was used to investigate the spatial and temporal dynamics of cortical activity modulated by offline hf-tRNS on performance on a motion direction discrimination task. We used EEG to measure the amplitude of motion-related VEPs over the parieto-occipital cortex, as well as oscillatory power spectral density (PSD) at rest. A time–frequency decomposition analysis was also performed to investigate the shift in event-related spectral perturbation (ERSP) in response to the motion stimuli between the pre- and post-stimulation period. The results showed that the accuracy of the motion direction discrimination task was not modulated by offline hf-tRNS. Although the motion task was able to elicit motion-dependent VEP components (P1, N2, and P2), none of them showed any significant change between pre- and post-stimulation. We also found a time-dependent increase of the PSD in alpha and beta bands regardless of the stimulation protocol. Finally, time–frequency analysis showed a modulation of ERSP power in the hf-tRNS condition for gamma activity when compared to pre-stimulation periods and Sham stimulation. Overall, these results show that offline hf-tRNS may induce moderate aftereffects in brain oscillatory activity.

scholarly journals Atmospheric Compensation of PRISMA Data by Means of a Learning Based Approach

2021 ◽  
Vol 13 (15) ◽  
pp. 2967
Author(s):  
Nicola Acito ◽  
Marco Diani ◽  
Gregorio Procissi ◽  
Giovanni Corsini
Keyword(s):  
Spectral Range ◽  
Near Infrared ◽  
Random Noise ◽  
Synthetic Data ◽  
Regression Function ◽  
Short Wave ◽  
Hyperspectral Data ◽  
Electromagnetic Spectrum ◽  
Great Opportunity ◽  
Atmospheric Compensation

Atmospheric compensation (AC) allows the retrieval of the reflectance from the measured at-sensor radiance and is a fundamental and critical task for the quantitative exploitation of hyperspectral data. Recently, a learning-based (LB) approach, named LBAC, has been proposed for the AC of airborne hyperspectral data in the visible and near-infrared (VNIR) spectral range. LBAC makes use of a parametric regression function whose parameters are learned by a strategy based on synthetic data that accounts for (1) a physics-based model for the radiative transfer, (2) the variability of the surface reflectance spectra, and (3) the effects of random noise and spectral miscalibration errors. In this work we extend LBAC with respect to two different aspects: (1) the platform for data acquisition and (2) the spectral range covered by the sensor. Particularly, we propose the extension of LBAC to spaceborne hyperspectral sensors operating in the VNIR and short-wave infrared (SWIR) portion of the electromagnetic spectrum. We specifically refer to the sensor of the PRISMA (PRecursore IperSpettrale della Missione Applicativa) mission, and the recent Earth Observation mission of the Italian Space Agency that offers a great opportunity to improve the knowledge on the scientific and commercial applications of spaceborne hyperspectral data. In addition, we introduce a curve fitting-based procedure for the estimation of column water vapor content of the atmosphere that directly exploits the reflectance data provided by LBAC. Results obtained on four different PRISMA hyperspectral images are presented and discussed.

scholarly journals Multi-focus Image Fusion Using an Effective Discrete Wavelet Transform Based Algorithm

2014 ◽  
Vol 14 (2) ◽  
pp. 102-108 ◽  
Author(s):  
Yong Yang ◽  
Shuying Huang ◽  
Junfeng Gao ◽  
Zhongsheng Qian
Keyword(s):  
Wavelet Transform ◽  
Image Fusion ◽  
Discrete Wavelet Transform ◽  
High Frequency ◽  
Low Frequency ◽  
Objective Evaluation ◽  
Discrete Wavelet ◽  
Evaluation Indexes ◽  
Fused Image ◽  
Focus Image

Abstract In this paper, by considering the main objective of multi-focus image fusion and the physical meaning of wavelet coefficients, a discrete wavelet transform (DWT) based fusion technique with a novel coefficients selection algorithm is presented. After the source images are decomposed by DWT, two different window-based fusion rules are separately employed to combine the low frequency and high frequency coefficients. In the method, the coefficients in the low frequency domain with maximum sharpness focus measure are selected as coefficients of the fused image, and a maximum neighboring energy based fusion scheme is proposed to select high frequency sub-bands coefficients. In order to guarantee the homogeneity of the resultant fused image, a consistency verification procedure is applied to the combined coefficients. The performance assessment of the proposed method was conducted in both synthetic and real multi-focus images. Experimental results demonstrate that the proposed method can achieve better visual quality and objective evaluation indexes than several existing fusion methods, thus being an effective multi-focus image fusion method.

scholarly journals Methods for estimating uncertainty in factor analytic solutions

2014 ◽  
Vol 7 (3) ◽  
pp. 781-797 ◽  
Author(s):  
P. Paatero ◽  
S. Eberly ◽  
S. G. Brown ◽  
G. A. Norris
Keyword(s):  
Environmental Protection Agency ◽  
Synthetic Data ◽  
Analytic Solutions ◽  
Data Sets ◽  
Random Errors ◽  
Data Set ◽  
Factor Analytic ◽  
Uncertainty Estimates ◽  
Multilinear Engine ◽  
Analytic Models

Abstract. The EPA PMF (Environmental Protection Agency positive matrix factorization) version 5.0 and the underlying multilinear engine-executable ME-2 contain three methods for estimating uncertainty in factor analytic models: classical bootstrap (BS), displacement of factor elements (DISP), and bootstrap enhanced by displacement of factor elements (BS-DISP). The goal of these methods is to capture the uncertainty of PMF analyses due to random errors and rotational ambiguity. It is shown that the three methods complement each other: depending on characteristics of the data set, one method may provide better results than the other two. Results are presented using synthetic data sets, including interpretation of diagnostics, and recommendations are given for parameters to report when documenting uncertainty estimates from EPA PMF or ME-2 applications.

Reverse time migration

Geophysics ◽  
1983 ◽  
Vol 48 (11) ◽  
pp. 1514-1524 ◽  
Author(s):  
Edip Baysal ◽  
Dan D. Kosloff ◽  
John W. C. Sherwood
Keyword(s):  
Wave Amplitude ◽  
Synthetic Data ◽  
Data Sets ◽  
Field Observations ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Migration Method ◽  
Zero Offset ◽  
Time Extrapolation

Migration of stacked or zero‐offset sections is based on deriving the wave amplitude in space from wave field observations at the surface. Conventionally this calculation has been carried out through a depth extrapolation. We examine the alternative of carrying out the migration through a reverse time extrapolation. This approach may offer improvements over existing migration methods, especially in cases of steeply dipping structures with strong velocity contrasts. This migration method is tested using appropriate synthetic data sets.

scholarly journals An Image Denoising Method with Enhancement of the Directional Features Based on Wavelet and SVD Transforms

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Min Wang ◽  
Zhen Li ◽  
Xiangjun Duan ◽  
Wei Li
Keyword(s):  
Wavelet Transform ◽  
Singular Value Decomposition ◽  
Image Denoising ◽  
High Frequency ◽  
Low Frequency ◽  
Singular Value ◽  
Denoising Method ◽  
Diagonal Part ◽  
Value Decomposition ◽  
Image Part

This paper proposes an image denoising method, using the wavelet transform and the singular value decomposition (SVD), with the enhancement of the directional features. First, use the single-level discrete 2D wavelet transform to decompose the noised image into the low-frequency image part and the high-frequency parts (the horizontal, vertical, and diagonal parts), with the edge extracted and retained to avoid edge loss. Then, use the SVD to filter the noise of the high-frequency parts with image rotations and the enhancement of the directional features: to filter the diagonal part, one needs first to rotate it 45 degrees and rotate it back after filtering. Finally, reconstruct the image from the low-frequency part and the filtered high-frequency parts by the inverse wavelet transform to get the final denoising image. Experiments show the effectiveness of this method, compared with relevant methods.

Application of complex-trace analysis to seismic data for random-noise suppression and temporal resolution improvement

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. V79-V86 ◽  
Author(s):  
Hakan Karsli ◽  
Derman Dondurur ◽  
Günay Çifçi
Keyword(s):  
Seismic Data ◽  
Trace Analysis ◽  
Noise Suppression ◽  
Single Channel ◽  
Random Noise ◽  
Synthetic Data ◽  
Low Frequency ◽  
Bright Spot ◽  
Phase Information ◽  
Resolution Improvement

Time-dependent amplitude and phase information of stacked seismic data are processed independently using complex trace analysis in order to facilitate interpretation by improving resolution and decreasing random noise. We represent seismic traces using their envelopes and instantaneous phases obtained by the Hilbert transform. The proposed method reduces the amplitudes of the low-frequency components of the envelope, while preserving the phase information. Several tests are performed in order to investigate the behavior of the present method for resolution improvement and noise suppression. Applications on both 1D and 2D synthetic data show that the method is capable of reducing the amplitudes and temporal widths of the side lobes of the input wavelets, and hence, the spectral bandwidth of the input seismic data is enhanced, resulting in an improvement in the signal-to-noise ratio. The bright-spot anomalies observed on the stacked sections become clearer because the output seismic traces have a simplified appearance allowing an easier data interpretation. We recommend applying this simple signal processing for signal enhancement prior to interpretation, especially for single channel and low-fold seismic data.

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