Noise reduction by vector median filtering

Geophysics ◽  
2013 ◽  
Vol 78 (3) ◽  
pp. V79-V87 ◽  
Author(s):  
Yike Liu
Keyword(s):  
Vector Field ◽  
Field Data ◽  
Vector Fields ◽  
Median Filter ◽  
Random Noise ◽  
Computation Time ◽  
Geophysical Data ◽  
Data Sets ◽  
Median Filtering ◽  
Vector Median

The scalar median filter (SMF) is often used to reduce noise in scalar geophysical data. We present an extension of the SMF to a vector median filter (VMF) for suppressing noise contained in geophysical data represented by multidimensional, multicomponent vector fields. Although the SMF can be applied to each component of a vector field individually, the VMF is applied to all components simultaneously. Like the SMF, the VMF intends to suppress random noise while preserving discontinuities in the vector fields. Preserving such discontinuities is essential for exploration geophysics because discontinuities often manifest important geologic features such as faults and stratigraphic channels. The VMF is applied to synthetic and field data sets. The results are compared to those generated by using SMF, f-x deconvolution, and mean filters. Our results indicate that the VMF can reduce noise while preserving discontinuities more effectively than the alternatives. In addition, a fast VMF algorithm is described for reducing computation time.

Rapid multi-scale analysis of near-surface geophysical anomaly maps: Application to an archaeo-geophysical data set

Geophysics ◽  
2020 ◽  
pp. 1-41 ◽  
Author(s):  
Jens Tronicke ◽  
Niklas Allroggen ◽  
Felix Biermann ◽  
Florian Fanselow ◽  
Julien Guillemoteau ◽  
...  
Keyword(s):  
Random Noise ◽  
Geophysical Data ◽  
Magnetic Data ◽  
Engineering Practice ◽  
Data Sets ◽  
Stripe Pattern ◽  
Data Set ◽  
Near Surface ◽  
Multi Scale ◽  
Topographic Data

In near-surface geophysics, ground-based mapping surveys are routinely employed in a variety of applications including those from archaeology, civil engineering, hydrology, and soil science. The resulting geophysical anomaly maps of, for example, magnetic or electrical parameters are usually interpreted to laterally delineate subsurface structures such as those related to the remains of past human activities, subsurface utilities and other installations, hydrological properties, or different soil types. To ease the interpretation of such data sets, we propose a multi-scale processing, analysis, and visualization strategy. Our approach relies on a discrete redundant wavelet transform (RWT) implemented using cubic-spline filters and the à trous algorithm, which allows to efficiently compute a multi-scale decomposition of 2D data using a series of 1D convolutions. The basic idea of the approach is presented using a synthetic test image, while our archaeo-geophysical case study from North-East Germany demonstrates its potential to analyze and process rather typical geophysical anomaly maps including magnetic and topographic data. Our vertical-gradient magnetic data show amplitude variations over several orders of magnitude, complex anomaly patterns at various spatial scales, and typical noise patterns, while our topographic data show a distinct hill structure superimposed by a microtopographic stripe pattern and random noise. Our results demonstrate that the RWT approach is capable to successfully separate these components and that selected wavelet planes can be scaled and combined so that the reconstructed images allow for a detailed, multi-scale structural interpretation also using integrated visualizations of magnetic and topographic data. Because our analysis approach is straightforward to implement without laborious parameter testing and tuning, computationally efficient, and easily adaptable to other geophysical data sets, we believe that it can help to rapidly analyze and interpret different geophysical mapping data collected to address a variety of near-surface applications from engineering practice and research.

Imaging diffractors using wave-equation migration

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. S459-S468 ◽  
Author(s):  
Lu Liu ◽  
Etienne Vincent ◽  
Xu Ji ◽  
Fuhao Qin ◽  
Yi Luo
Keyword(s):  
Wave Equation ◽  
Field Data ◽  
Recursive Algorithm ◽  
Median Filter ◽  
Random Noise ◽  
Plane Waves ◽  
Computationally Efficient ◽  
Imaging Point ◽  
Local Plane ◽  
Dip Angle

We have developed a fast and practical wave-equation-based migration method to image subsurface diffractors. The method is composed of three steps in our implementation. First, it decomposes extrapolated receiver wavefields at every imaging point into local plane waves by a linear Radon transform; the transform is realized by a novel computationally efficient recursive algorithm. Second, the decomposed plane waves are zero lag-correlated with the incident source wavefields, where the incident angles are computed via the structure tensor approach. The resulting prestack images are binned into dip-angle gathers according to the directions of the decomposed plane waves and the calculated incident angles. Third, a windowed median filter is applied to the dip-angle gathers to suppress the focused reflection energy, and it produces the desired diffraction images. This method is tested on synthetic and field data. The results demonstrate that it is resistant to random noise, computationally efficient, and applicable to field data in practice. The results also indicate that the diffraction images are able to provide important discontinuous geologic features, such as scattering and faulting zones, and thus are helpful for seismic interpretation.

Random noise attenuation by 3D Multi-directional vector median filter

2018 ◽  
Vol 159 ◽  
pp. 277-284 ◽  
Author(s):  
Shaojiang Wu ◽  
Yibo Wang ◽  
Zhixin Di ◽  
Xu Chang
Keyword(s):  
Median Filter ◽  
Random Noise ◽  
Noise Attenuation ◽  
Random Noise Attenuation ◽  
Vector Median

scholarly journals Flattening without picking

Geophysics ◽  
2006 ◽  
Vol 71 (4) ◽  
pp. P13-P20 ◽  
Author(s):  
Jesse Lomask ◽  
Antoine Guitton ◽  
Sergey Fomel ◽  
Jon Claerbout ◽  
Alejandro A. Valenciano
Keyword(s):  
Seismic Data ◽  
Field Data ◽  
Fourier Transforms ◽  
Computation Time ◽  
Fault Model ◽  
Data Sets ◽  
Iterative Approach ◽  
Iteratively Reweighted Least Squares ◽  
Fault Indicator ◽  
Full Volume

We present an efficient full-volume automatic dense-picking method for flattening seismic data. First local dips (stepouts) are calculated over the entire seismic volume. The dips are then resolved into time shifts (or depth shifts) using a nonlinear Gauss-Newton iterative approach that exploits fast Fourier transforms to minimize computation time. To handle faults (discontinuous reflections), we apply a weighted inversion scheme. The weight identifies locations of faults, allowing dips to be summed around the faults to reduce the influence of erroneous dip estimates near the fault. If a fault model is not provided, we can estimate a suitable weight (essentially a fault indicator) within our inversion using an iteratively reweighted least squares (IRLS) method. The method is tested successfully on both synthetic and field data sets of varying degrees of complexity, including salt piercements, angular unconformities, and laterally limited faults.

scholarly journals Ameliorated mean adaptive median filtering algorithm

2019 ◽  
Vol 118 ◽  
pp. 02069
Author(s):  
Hongming Zhang ◽  
Yongping Wang ◽  
Chuang Peng
Keyword(s):  
Median Filter ◽  
Random Noise ◽  
Infrared Image ◽  
Electrical Equipment ◽  
Median Filtering ◽  
Salt And Pepper Noise ◽  
Filtering Algorithm ◽  
Average Value ◽  
Adaptive Median Filter ◽  
Salt And Pepper

Aiming at the problem that the quality of infrared image decreases due to the large amount of random noise in the process of collection and transmission of infrared image of electrical equipment, and the accuracy of automatic detection of electrical equipment decreases, based on the traditional adaptive median filter algorithm, the adaptive median filter is analyzed, which can filter only the salt and pepper noise below 25%. An improved mean adaptive median filtering algorithm is proposed to overcome the shortcomings of wave effect. Firstly, the filtering window is selected according to the decision setting condition, and then it is judged whether the K-mean value near the center point is a noise point, and if so, the window is increased, otherwise the average value is output. Finally, it is judged whether the value of the current pixel point is noise, and if so, the average value is output, otherwise, the current pixel value is output. The experimental results show that the algorithm can effectively filter salt and pepper noise and Gauss noise, while maintaining the image sharpness, and has good filtering performance on PSNR and MSE indicators.

An Alternate Algorithm for (3x3) Median Filtering of Digital Images

2012 ◽  
Vol 2 (1) ◽  
pp. 7-9 ◽  
Author(s):  
Satinderjit Singh
Keyword(s):  
Median Filter ◽  
Computational Cost ◽  
Spatial Coherence ◽  
General Purpose ◽  
Median Filtering ◽  
Basic Algorithm ◽  
Temporal Complexity ◽  
Filter Kernel ◽  
One Step ◽  
High Computational Cost

Median filtering is a commonly used technique in image processing. The main problem of the median filter is its high computational cost (for sorting N pixels, the temporal complexity is O(N·log N), even with the most efficient sorting algorithms). When the median filter must be carried out in real time, the software implementation in general-purpose processorsdoes not usually give good results. This Paper presents an efficient algorithm for median filtering with a 3x3 filter kernel with only about 9 comparisons per pixel using spatial coherence between neighboring filter computations. The basic algorithm calculates two medians in one step and reuses sorted slices of three vertical neighboring pixels. An extension of this algorithm for 2D spatial coherence is also examined, which calculates four medians per step.

scholarly journals Pairings between bounded divergence-measure vector fields and BV functions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Graziano Crasta ◽  
Virginia De Cicco ◽  
Annalisa Malusa
Keyword(s):  
Vector Field ◽  
Conservation Laws ◽  
Bounded Variation ◽  
Vector Fields ◽  
Hyperbolic Conservation Laws ◽  
Divergence Measure ◽  
Compensated Compactness ◽  
Hyperbolic Conservation ◽  
Bv Functions ◽  
Bounded Functions

AbstractWe introduce a family of pairings between a bounded divergence-measure vector field and a function u of bounded variation, depending on the choice of the pointwise representative of u. We prove that these pairings inherit from the standard one, introduced in [G. Anzellotti, Pairings between measures and bounded functions and compensated compactness, Ann. Mat. Pura Appl. (4) 135 1983, 293–318], [G.-Q. Chen and H. Frid, Divergence-measure fields and hyperbolic conservation laws, Arch. Ration. Mech. Anal. 147 1999, 2, 89–118], all the main properties and features (e.g. coarea, Leibniz, and Gauss–Green formulas). We also characterize the pairings making the corresponding functionals semicontinuous with respect to the strict convergence in \mathrm{BV}. We remark that the standard pairing in general does not share this property.

scholarly journals A Review of Geophysical Modeling Based on Particle Swarm Optimization

2021 ◽  
Author(s):  
Francesca Pace ◽  
Alessandro Santilano ◽  
Alberto Godio
Keyword(s):  
Particle Swarm Optimization ◽  
Inverse Modeling ◽  
Critical Evaluation ◽  
Particle Swarm ◽  
Geophysical Data ◽  
Magnetic Data ◽  
Data Sets ◽  
Swarm Optimization ◽  
Geophysical Modeling ◽  
Original Works

AbstractThis paper reviews the application of the algorithm particle swarm optimization (PSO) to perform stochastic inverse modeling of geophysical data. The main features of PSO are summarized, and the most important contributions in several geophysical fields are analyzed. The aim is to indicate the fundamental steps of the evolution of PSO methodologies that have been adopted to model the Earth’s subsurface and then to undertake a critical evaluation of their benefits and limitations. Original works have been selected from the existing geophysical literature to illustrate successful PSO applied to the interpretation of electromagnetic (magnetotelluric and time-domain) data, gravimetric and magnetic data, self-potential, direct current and seismic data. These case studies are critically described and compared. In addition, joint optimization of multiple geophysical data sets by means of multi-objective PSO is presented to highlight the advantage of using a single solver that deploys Pareto optimality to handle different data sets without conflicting solutions. Finally, we propose best practices for the implementation of a customized algorithm from scratch to perform stochastic inverse modeling of any kind of geophysical data sets for the benefit of PSO practitioners or inexperienced researchers.

scholarly journals The geometry of null-like disformal transformations

2019 ◽  
Vol 16 (11) ◽  
pp. 1950180 ◽  
Author(s):  
I. P. Lobo ◽  
G. G. Carvalho
Keyword(s):  
Vector Field ◽  
Conformal Transformation ◽  
Vector Fields ◽  
Killing Vector ◽  
Killing Vector Fields ◽  
Spinor Structure ◽  
Schwarzschild Metric ◽  
Killing Vectors ◽  
Symmetry Properties ◽  
Geometric Objects

Motivated by the hindrance of defining metric tensors compatible with the underlying spinor structure, other than the ones obtained via a conformal transformation, we study how some geometric objects are affected by the action of a disformal transformation in the closest scenario possible: the disformal transformation in the direction of a null-like vector field. Subsequently, we analyze symmetry properties such as mutual geodesics and mutual Killing vectors, generalized Weyl transformations that leave the disformal relation invariant, and introduce the concept of disformal Killing vector fields. In most cases, we use the Schwarzschild metric, in the Kerr–Schild formulation, to verify our calculations and results. We also revisit the disformal operator using a Newman–Penrose basis to show that, in the null-like case, this operator is not diagonalizable.

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