Influence of refraction to the accuracy of a solution for the 2D-emission tomography problem
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Abstract
- We suggest two numerical methods for solving a 2D-emission tomography problem. One of them bases on the approach of best approximation, the other is the algorithm of approximate inverse, which represents a stable regularization scheme for linear ill-posed problems. The mathematical model of emission tomography is given by the exponential ray transform (ERT). The aim of this paper is on the one hand a comparison of both methods by applying them on the inversion of the ERT with constant absorption, and on the other hand the investigation of the reconstruction accuracy, if we have some refraction or absorption within the object under consideration. Several numerical test series quantify the influence of refraction and absorption to the solution and answer some questions, which come from related problems.
© 2013 by Walter de Gruyter GmbH & Co.
Articles in the same Issue
- CONTENTS
- Some problems of the theory of multidimensional inverse problems
- Complex force fields and complex orbits
- Influence of refraction to the accuracy of a solution for the 2D-emission tomography problem
- An iterated version of Lavrent’iev’s method for ill-posed equations with approximately specified data
- Finding small inhomogeneities from scattering data
- An inverse problem for orthotropic medium
Articles in the same Issue
- CONTENTS
- Some problems of the theory of multidimensional inverse problems
- Complex force fields and complex orbits
- Influence of refraction to the accuracy of a solution for the 2D-emission tomography problem
- An iterated version of Lavrent’iev’s method for ill-posed equations with approximately specified data
- Finding small inhomogeneities from scattering data
- An inverse problem for orthotropic medium
