scholarly journals On a method of image reconstruction of anisotropic media using applied quasipotential tomographic data

2019 ◽  
Vol 6 (2) ◽  
pp. 211-219
Author(s):  
A. Ya. Bomba ◽  
◽  
M. T. Kuzlo ◽  
O. R. Michuta ◽  
M. V. Boichura ◽  
...  
Keyword(s):  
Image Reconstruction ◽  
Anisotropic Media ◽  
Tomographic Data

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

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 APPLIED QUASIPOTENTIAL METHOD FOR SOLVING THE COEFFICIENT PROBLEMS OF PARAMETER IDENTIFICATION OF ANISOTROPIC MEDIA

2019 ◽  
Vol 9 (1) ◽  
pp. 33-36 ◽  
Author(s):  
Andrii Bomba ◽  
Andrij Safonyk ◽  
Olha Michuta ◽  
Mykhailo Boichura
Keyword(s):  
Parameter Identification ◽  
Numerical Method ◽  
Anisotropic Medium ◽  
Numerical Experiments ◽  
Anisotropic Media ◽  
Quasiconformal Mappings ◽  
Conductivity Tensor ◽  
Coefficient Problems ◽  
Tomographic Data

A numerical method of quasiconformal mappings for solving the coefficient problems of finding eigenvalues of the conductivity tensor having information about its directions in an anisotropic medium using applied quasipotential tomographic data is generalized. The corresponding algorithm is based on the alternate solving of problems on quasiconformal mappings and parameter identification. The results of numerical experiments of imitative restoration of environment structure are presented.

Truncated Hilbert transform and image reconstruction from limited tomographic data

2006 ◽  
Vol 22 (3) ◽  
pp. 1037-1053 ◽  
Author(s):  
Michel Defrise ◽  
Frédéric Noo ◽  
Rolf Clackdoyle ◽  
Hiroyuki Kudo
Keyword(s):  
Image Reconstruction ◽  
Hilbert Transform ◽  
Tomographic Data

scholarly journals Template-Based Image Reconstruction from Sparse Tomographic Data

2019 ◽  
Vol 82 (3) ◽  
pp. 1081-1109 ◽  
Author(s):  
Lukas F. Lang ◽  
Sebastian Neumayer ◽  
Ozan Öktem ◽  
Carola-Bibiane Schönlieb
Keyword(s):  
Image Reconstruction ◽  
Image Registration ◽  
Cross Correlation ◽  
Distance Functions ◽  
X Ray ◽  
Template Image ◽  
X Ray Computed ◽  
Tomographic Data ◽  
Noisy Measurements ◽  
Theoretical Results

Abstract We propose a variational regularisation approach for the problem of template-based image reconstruction from indirect, noisy measurements as given, for instance, in X-ray computed tomography. An image is reconstructed from such measurements by deforming a given template image. The image registration is directly incorporated into the variational regularisation approach in the form of a partial differential equation that models the registration as either mass- or intensity-preserving transport from the template to the unknown reconstruction. We provide theoretical results for the proposed variational regularisation for both cases. In particular, we prove existence of a minimiser, stability with respect to the data, and convergence for vanishing noise when either of the abovementioned equations is imposed and more general distance functions are used. Numerically, we solve the problem by extending existing Lagrangian methods and propose a multilevel approach that is applicable whenever a suitable downsampling procedure for the operator and the measured data can be provided. Finally, we demonstrate the performance of our method for template-based image reconstruction from highly undersampled and noisy Radon transform data. We compare results for mass- and intensity-preserving image registration, various regularisation functionals, and different distance functions. Our results show that very reasonable reconstructions can be obtained when only few measurements are available and demonstrate that the use of a normalised cross correlation-based distance is advantageous when the image intensities between the template and the unknown image differ substantially.

Image reconstruction of optical tomographic data from a highly scattering medium

2001 ◽  
Author(s):  
Junwon Lee ◽  
Donald W. Wilson ◽  
Harrison H. Barrett ◽  
Arthur F. Gmitro
Keyword(s):  
Image Reconstruction ◽  
Scattering Medium ◽  
Tomographic Data ◽  
Highly Scattering Medium
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