scholarly journals Spatial Analogues of Numerical Quasiconformal Mapping Methods for Solving Problems of Bursts Parameters Identification

2020 ◽  
pp. 11-14
Author(s):  
Mykhailo Boichura
Keyword(s):  
Image Reconstruction ◽  
Quasiconformal Mapping ◽  
Numerical Experiments ◽  
Domain Boundary ◽  
Three Dimensional ◽  
Parameters Identification ◽  
Dimensional Case ◽  
Flow Function ◽  
Flow Lines ◽  
Tomographic Data

An approach to solving the problem of image reconstruction based on applied quasipotential tomographic data in the three-dimensional case is developed. It is based on the synthesis of spatial analogues of numerical quasiconformal mapping methods and algorithm for identifying the parameters of local bursts of homogeneous materials using similar methods on the plane. The peculiarity of the corresponding algorithm is taking into account (for each of the appropriate injections) the presence of only equipotential lines (with given values of the flow function or distributions of local velocities on them) and flow lines (with known potential distributions on them) at the domain boundary. Numerical experiments of simulative restoration of the environment structure are carried out.

scholarly journals Spatial Analogues of Numerical Quasiconformal Mapping Methods for Solving Identification Problems in Anisotropic Media

2019 ◽  
pp. 19-20
Author(s):  
Mykhailo Boichura ◽  
Olha Michuta ◽  
Andrii Bomba
Keyword(s):  
Image Reconstruction ◽  
Differential Equations ◽  
Quasiconformal Mapping ◽  
Complex Analysis ◽  
A Priori ◽  
Anisotropic Media ◽  
Identification Problems ◽  
Stream Functions ◽  
Tomographic Data ◽  
Spatial Bodies

The approach to solving the gradient problems of image reconstruction of spatial bodies using applied quasipotential tomographic data that is based on numerical complex analysis methods is extended to cases of anisotropic media. Here the distribution of eigen-directions of the conductivity tensor is considered a priori known. We propose to identify the parameters of the corresponding quasiideal stream by the way of minimizing the functional of the sum of squares of residuals which constructed using differential equations in partial derivatives that relate the quasipotential of velocity and the spatially quasicomplex conjugated stream functions

On the theory of Langmuir solitons

1977 ◽  
Vol 17 (2) ◽  
pp. 153-170 ◽  
Author(s):  
J. Gibbons ◽  
S. G. Thornhill ◽  
M. J. Wardrop ◽  
D. Ter Haar
Keyword(s):  
Conservation Laws ◽  
Numerical Experiments ◽  
Lagrangian Density ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Turbulent Plasma ◽  
Dimensional Case ◽  
One Dimensional ◽  
The One ◽  
Langmuir Solitons

We find a Lagrangian density from which the equations of motion for the Lang-muir solitons follow in the usual way. We show how this Lagrangian leads to the usual conservation laws. For the one-dimensional case we discuss how a consideration of these conservation laws can help us to understand some of the results obtained in numerical experiments on the behaviour of a strongly turbulent plasma. We point out that the situation in the three-dimensional case may be fundamentally different, and we discuss near-sonic perturbations and Karpman's treatment of these.

Criteria and Methods for Reliable Three-Dimensional Image Reconstruction

1974 ◽  
Vol 32 ◽  
pp. 330-331
Author(s):  
R. A. Crowther
Keyword(s):  
Image Reconstruction ◽  
Finite Number ◽  
Density Distribution ◽  
Electron Micrographs ◽  
Mathematical Problem ◽  
Three Dimensional ◽  
Ideal Case ◽  
Dimensional Image ◽  
General Object ◽  
The Ideal

The reconstruction of a three-dimensional image of a specimen from a set of electron micrographs reduces, under certain assumptions about the imaging process in the microscope, to the mathematical problem of reconstructing a density distribution from a set of its plane projections.In the absence of noise we can formulate a purely geometrical criterion, which, for a general object, fixes the resolution attainable from a given finite number of views in terms of the size of the object. For simplicity we take the ideal case of projections collected by a series of m equally spaced tilts about a single axis.

Three dimensional deblurring of transmitted-light brightfield micrographs

1993 ◽  
Vol 51 ◽  
pp. 564-565
Author(s):  
Santosh Bhattacharyya
Keyword(s):  
Image Reconstruction ◽  
Three Dimensional ◽  
Transmitted Light ◽  
Reconstruction Algorithms ◽  
3D Image Reconstruction ◽  
Structural Details ◽  
Spread Function ◽  
Early Testing ◽  
Linearized Model ◽  
Image Reconstruction Algorithms

Three dimensional microscopic structures play an important role in the understanding of various biological and physiological phenomena. Structural details of neurons, such as the density, caliber and volumes of dendrites, are important in understanding physiological and pathological functioning of nervous systems. Even so, many of the widely used stains in biology and neurophysiology are absorbing stains, such as horseradish peroxidase (HRP), and yet most of the iterative, constrained 3D optical image reconstruction research has concentrated on fluorescence microscopy. It is clear that iterative, constrained 3D image reconstruction methodologies are needed for transmitted light brightfield (TLB) imaging as well. One of the difficulties in doing so, in the past, has been in determining the point spread function of the system.We have been developing several variations of iterative, constrained image reconstruction algorithms for TLB imaging. Some of our early testing with one of them was reported previously. These algorithms are based on a linearized model of TLB imaging.

scholarly journals Three-Dimensional Elastodynamic Analysis Employing Partially Discontinuous Boundary Elements

Algorithms ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 129
Author(s):  
Yuan Li ◽  
Ni Zhang ◽  
Yuejiao Gong ◽  
Wentao Mao ◽  
Shiguang Zhang
Keyword(s):  
Side Effect ◽  
Domain Boundary ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Integration Scheme ◽  
Computational Accuracy ◽  
Time Step ◽  
Corner Points ◽  
Discontinuous Elements ◽  
The Time Domain

Compared with continuous elements, discontinuous elements advance in processing the discontinuity of physical variables at corner points and discretized models with complex boundaries. However, the computational accuracy of discontinuous elements is sensitive to the positions of element nodes. To reduce the side effect of the node position on the results, this paper proposes employing partially discontinuous elements to compute the time-domain boundary integral equation of 3D elastodynamics. Using the partially discontinuous element, the nodes located at the corner points will be shrunk into the element, whereas the nodes at the non-corner points remain unchanged. As such, a discrete model that is continuous on surfaces and discontinuous between adjacent surfaces can be generated. First, we present a numerical integration scheme of the partially discontinuous element. For the singular integral, an improved element subdivision method is proposed to reduce the side effect of the time step on the integral accuracy. Then, the effectiveness of the proposed method is verified by two numerical examples. Meanwhile, we study the influence of the positions of the nodes on the stability and accuracy of the computation results by cases. Finally, the recommended value range of the inward shrink ratio of the element nodes is provided.

Acceleration of the EM-like reconstruction method for diffuse optical tomography with ordered-subsets method

2014 ◽  
Vol 22 (3) ◽  
Author(s):  
Caifang Wang
Keyword(s):  
Numerical Experiments ◽  
Imaging Modality ◽  
Random Medium ◽  
Optical Tomography ◽  
Back Propagation ◽  
Three Dimensional ◽  
Diffuse Optical Tomography ◽  
Optical Parameters ◽  
Reconstruction Method ◽  
Boundary Measurements

Abstract.Diffuse optical tomography (DOT) is an optical imaging modality, which provides the spatial distribution of the optical parameters inside a random medium. A propagation back-propagation method named EM-like reconstruction method for stationary DOT problem has been proposed yet. This method is really time consuming. Hence the ordered-subsets (OS) technique for this reconstruction method is studied in this paper. The boundary measurements of DOT are grouped into nonoverlapping and overlapping ordered sequence of subsets with random partition, sequential partition and periodic partition, respectively. The performance of OS methods is compared with the standard EM-like reconstruction method with two-dimensional and three-dimensional numerical experiments. The numerical experiments indicate that reconstruction of nonoverlapping subsets with periodic partition, overlapping subsets with periodic partition and standard EM-like method provide very similar acceptable reconstruction results. However, reconstruction of nonoverlapping subsets with periodic partition spends a minimum of time to get proper results.

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