scholarly journals Fourier Transforms of Real Data in Two and Three Dimensions

1989 ◽  
Vol 3 (5) ◽  
pp. 84 ◽  
Author(s):  
William H. Press ◽  
Saul A. Teukolsky
Keyword(s):  
Fourier Transforms ◽  
Real Data ◽  
Three Dimensions

scholarly journals G-Tric: generating three-way synthetic datasets with triclustering solutions

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
João Lobo ◽  
Rui Henriques ◽  
Sara C. Madeira
Keyword(s):  
State Of The Art ◽  
Synthetic Data ◽  
Ground Truth ◽  
Real Data ◽  
Three Dimensions ◽  
Additional Advantage ◽  
Urban Dynamics ◽  
Data Generator ◽  
Real World Datasets ◽  
Synthetic Datasets

Abstract Background Three-way data started to gain popularity due to their increasing capacity to describe inherently multivariate and temporal events, such as biological responses, social interactions along time, urban dynamics, or complex geophysical phenomena. Triclustering, subspace clustering of three-way data, enables the discovery of patterns corresponding to data subspaces (triclusters) with values correlated across the three dimensions (observations $$\times$$ × features $$\times$$ × contexts). With increasing number of algorithms being proposed, effectively comparing them with state-of-the-art algorithms is paramount. These comparisons are usually performed using real data, without a known ground-truth, thus limiting the assessments. In this context, we propose a synthetic data generator, G-Tric, allowing the creation of synthetic datasets with configurable properties and the possibility to plant triclusters. The generator is prepared to create datasets resembling real 3-way data from biomedical and social data domains, with the additional advantage of further providing the ground truth (triclustering solution) as output. Results G-Tric can replicate real-world datasets and create new ones that match researchers needs across several properties, including data type (numeric or symbolic), dimensions, and background distribution. Users can tune the patterns and structure that characterize the planted triclusters (subspaces) and how they interact (overlapping). Data quality can also be controlled, by defining the amount of missing, noise or errors. Furthermore, a benchmark of datasets resembling real data is made available, together with the corresponding triclustering solutions (planted triclusters) and generating parameters. Conclusions Triclustering evaluation using G-Tric provides the possibility to combine both intrinsic and extrinsic metrics to compare solutions that produce more reliable analyses. A set of predefined datasets, mimicking widely used three-way data and exploring crucial properties was generated and made available, highlighting G-Tric’s potential to advance triclustering state-of-the-art by easing the process of evaluating the quality of new triclustering approaches.

Robustness of Anatomically Guided Pixel-by-Pixel Algorithms for Partial Volume Effect Correction in Positron Emission Tomography

1999 ◽  
Vol 19 (5) ◽  
pp. 547-559 ◽  
Author(s):  
Daniel Strul ◽  
Bernard Bendriem
Keyword(s):  
Positron Emission Tomography ◽  
Real Data ◽  
Volume Effect ◽  
Performance Criterion ◽  
Three Dimensions ◽  
Emission Tomography ◽  
Tissue Segmentation ◽  
Positron Emission ◽  
Current Article ◽  
Effective Use

Several algorithms have been proposed to improve positron emission tomography quantification by combining anatomical and functional information in a pixel-by-pixel correction scheme. The precision of these methods when applied to real data depends on the precision of the manifold correction steps, such as full-width half-maximum modeling, magnetic resonance imaging-positron emission tomography registration, tissue segmentation, or background activity estimation. A good understanding of the influence of these parameters thus is critical to the effective use of the algorithms. In the current article, the authors present a monodimensional model that allows a simple theoretical and experimental evaluation of correction imprecision. The authors then assess correction robustness in three dimensions with computer simulations, and evaluate the validity of regional SD as a correction performance criterion.

3D VSP migration by image point transform

Geophysics ◽  
2010 ◽  
Vol 75 (3) ◽  
pp. S121-S130 ◽  
Author(s):  
Calin Cosma ◽  
Lucian Balu ◽  
Nicoleta Enescu
Keyword(s):  
Mineral Exploration ◽  
Real Data ◽  
Three Dimensions ◽  
Seismic Survey ◽  
Image Point ◽  
Inverse Transform ◽  
Time Distance ◽  
Diffraction Patterns ◽  
Original Time ◽  
Downhole Measurements

The common characteristic of the seismic methods involving downhole measurements is the difficulty of designing surveys able to image the subsurface space evenly. Migration schemes for these layouts are sensitive to reconstruction artifacts. The defining property of the image point (IP) transform is its ability to accumulate amplitudes of curved reflection events appearing in time-distance profiles into approximately discoidal (or spherical in three dimensions) vicinities in the IP domain. Due to the reflected wavefields collapsing into such vicinities in the IP domain, the emphasizing of the reflectors consists of enhancing regions with higher amounts of accumulated amplitude. True-dip filtering can also easily be performed, even for reflectors appearing in the time-distance profiles as curved events due to their dip, source offset or variable velocity field. Reflecting interfaces aredefined as sets of linked piecewise planar-reflector elements rather than as collections of point diffractors. True reflectors fitting this description are enhanced by the IP transform while diffraction patterns, events produced by other wave types, multiples, and noise of any kind, tend to be suppressed. The inverse transform leads to filtered versions of time-distance profiles. An alternative to performing the inverse transform back to the original time-distance representation is computing 2D/3D migrated images directly from the transformed IP space. Although the 3D migration by IP transform is applicable to any seismic survey geometry, we focused on procedures for enhancing prestack migrated images obtained by sparse multioffset, multiazimuth vertical seismic profiling (VSP) surveys as typically performed for mining site characterization and mineral exploration. The real data used were collected within an extensive mining seismic investigation program performed in Canada.

scholarly journals Standardised Metrics and Methods for Synthetic Tabular Data Evaluation

2021 ◽  
Author(s):  
Mikel Hernandez ◽  
Gorka Epelde ◽  
Ane Alberdi ◽  
Rodrigo Cilla ◽  
Debbie Rankin
Keyword(s):  
Scientific Community ◽  
Real Data ◽  
Three Dimensions ◽  
Great Promise ◽  
Data Generation ◽  
Tabular Data ◽  
Trade Off ◽  
Analysis And Evaluation ◽  
Extensive Analysis ◽  
Objective Metrics

Synthetic Tabular Data Generation (STDG) is a potentially valuable technology with great promise to augment real data and preserve privacy. However, prior to adoption, an empirical assessment of synthetic tabular data (STD) is required across the three dimensions of resemblance, utility, and privacy, trying to find a trade-off between them. A lack of standardised and objective metrics and methods has been found targeting this assessment in the literature and neither an organised pipeline or process for coordinating this evaluation has been identified. Therefore, in this work we propose a collection of metrics and methods to evaluate STD in the previously defined dimensions, presenting a meaningful orchestration of them and a pipeline unifying all of them. Additionally, we present a methodology to categorise STDG approaches performance for each dimension. Finally, we conducted an extensive analysis and evaluation to verify the usability of the proposed pipeline across six healthcare-related datasets, using four STDG approaches. The results of these analyses showed that the proposed pipeline can effectively be used to evaluate and benchmark the STD generated with one or more different STDG approaches, helping the scientific community to select the most suitable approaches for their data and application of interest.

Application of three-dimensional kinematic imaging to analysis of seismic reflection data from the Nevada Test Site

1984 ◽  
Vol 74 (6) ◽  
pp. 2187-2199
Author(s):  
Jing Wen ◽  
George A. McMechan
Keyword(s):  
Grid Point ◽  
Three Dimensional ◽  
Real Data ◽  
Test Site ◽  
Three Dimensions ◽  
Seismic Survey ◽  
Nevada Test Site ◽  
Seismic Reflection Data ◽  
Reflector Surface ◽  
Best Fit

Abstract Three-dimensional kinematic migration produces a “best-fit” migrated surface, in three-dimensions, of any chosen reflector. The data are the travel times of all observed reflections and diffractions produced by the reflector. Source/receiver configurations are arbitrary, but should be arranged to provide good spatial sampling of the reflector. Each observation contributes an ellipsoid containing all possible reflection points. From this family of ellipsoids, the optimal reflector surface (the envelope of the family) is estimated by use of a statistical imaging condition. The “best-fit” position and shape of the reflector surface is obtained by defining a regular (x, y) grid over the region of interest and estimating the reflector depth beneath each grid point from the distribution of ellipsoids that are present there. The imaging criterion is implemented at each grid point by convolution of a Gaussian with the vector of ellipsoid depths. The width of the Gaussian is chosen to correspond to the scale of the features one wishes to resolve in the image. For each grid point, the migrated image is located at the depth at which the convolution is a maximum. The algorithm is applied to both synthetic and real data. The synthetic data are constructed by ray tracing in a known structure. The real data are from a seismic survey at the Nevada Test Site; here, a reflector is imaged and interpreted as the surface of a high velocity Paleozoic dolomite that is overlain by low-velocity tuffs.

Visualizing Latent Class Models with Analysis-of-distance BIPLOTS

2017 ◽  
Vol 47 (1) ◽  
pp. 345-378 ◽  
Author(s):  
Zsuzsa Bakk ◽  
Niel J. le Roux
Keyword(s):  
Relative Density ◽  
Latent Class ◽  
Real Data ◽  
Latent Class Models ◽  
Three Dimensions ◽  
Categorical Analysis ◽  
Class Models

The authors propose using categorical analysis-of-distance biplots to visualize the posterior classifications arising from a latent class (LC) model. Using this multivariate plot, it is possible to visualize in two (or three) dimensions the profile of multiple LCs, specifically both the within- and between-class variation, and the overlap or separation of the classes together with the class weights. Furthermore, visualization of the relative density of each of the data patterns associated with a class is possible. The authors illustrate this approach with real data examples of LC models with three and more classes.

Efficient simultaneous wave-equation statics and trace regularization by series approximation

Geophysics ◽  
2010 ◽  
Vol 75 (3) ◽  
pp. U19-U28 ◽  
Author(s):  
Robert J. Ferguson
Keyword(s):  
Wave Equation ◽  
Gradient Methods ◽  
Synthetic Data ◽  
Real Data ◽  
Three Dimensions ◽  
Velocity Variation ◽  
Acceptable Solution ◽  
Direct Inversion ◽  
Data Inversion ◽  
Series Approximation

To address the problems of irregular trace spacing and statics correction, simultaneous regularization and wave-equation statics (WE statics) are implemented by least-squares inversion. In general, inversion is found to be intractable in three dimensions, so series approximation is made to reduce significantly the number of required integrals. The resulting operator is suitable for direct inversion or for use with gradient methods. Real and synthetic data are used to determine the viability of the inversion. For synthetic data, even for severe velocity variation and topography, inversion converges to an acceptable solution, and aliasing is reduced significantly. Similarly, for real data, inversion is found to return an antialiased, regularized result with WE statics applied.

3-D interpretation of reflected arrival times by finite‐difference techniques

Geophysics ◽  
1994 ◽  
Vol 59 (5) ◽  
pp. 844-849 ◽  
Author(s):  
M. Ali Riahi ◽  
Christopher Juhlin
Keyword(s):  
Finite Difference ◽  
Finite Difference Methods ◽  
Real Data ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Computationally Efficient ◽  
Reflected Waves ◽  
Arrival Times ◽  
First Arrival ◽  
Difference Methods

Finite‐difference methods have generally been used to solve dynamic wave propagation problems over the last 25 years (Alterman and Karal, 1968; Boore, 1972; Kelly et al., 1976; and Levander, 1988). Recently, finite‐difference methods have been applied to the eikonal equation to calculate the kinematic solution to the wave equation (Vidale, 1988 and 1990; Podvin and Lecomte, 1991; Van Trier and Symes, 1991; Qin et al., 1992). The calculation of the first‐arrival times using this method has proven to be considerably faster than using classical ray tracing, and problems such as shadow zones, multipathing, and barrier penetration are easily handled. Podvin and Lecomte (1991) and Matsuoka and Ezaka (1992) extended and expanded upon Vidale’s (1988) algorithm to calculate traveltimes for reflected waves in two dimensions. Based on finite‐difference calculations for first‐arrival times, Hole et al. (1992) devised a scheme for inverting synthetic and real data to estimate the depth to refractors in the crust in three dimensions. The method of Hole et al. (1992) for inversion is computationally efficient since it avoids the matrix inversion of many of the published schemes for refraction and reflection traveltime data (Gjøystdal and Ursin, 1981).

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