The method of approximate inverse for the normal Radon transform operator
Authors:
Open Access
- 1 January 2021
- conference paper
- Published by IOP Publishing in Journal of Physics: Conference Series
- Vol. 1715 (1) , 012048
Abstract
We propose an approach for reconstructing a three-dimensional function from the known values of the Radon transform. The approach is based on the method of approximate inverse. The result obtained is the basis of two approaches for reconstructing a potential part of the vector and symmetric 2-tensor fields from the known values of the normal Radon transform. The first approach allows the recovery of components of the potential part of fields, and the second one reconstructs a potential of the potential part of fields.Keywords
This publication has 14 references indexed in Scilit:
- Reconstruction of a Vector Field in a Ball from its Normal Radon TransformJournal of Mathematical Sciences, 2015
- Defect correction in vector field tomography: detecting the potential part of a field using BEM and implementation of the methodInverse Problems, 2004
- The approximate inverse in action III: 3D-Doppler tomographyNumerische Mathematik, 2004
- Influence of refraction to the accuracy of a solution for the 2D-emission tomography problemJournal of Inverse and Ill-posed Problems, 2000
- The Approximate Inverse in Action with an Application to Computerized TomographySIAM Journal on Numerical Analysis, 2000
- A novel filter design technique in 2D computerized tomographyInverse Problems, 1996
- Approximate inverse for linear and some nonlinear problemsInverse Problems, 1996
- A mollifier method for linear operator equations of the first kindInverse Problems, 1990
- Orthogonal Function Series Expansions and the Null Space of the Radon TransformSIAM Journal on Mathematical Analysis, 1984
- The method of orthogonal projection in potential theoryDuke Mathematical Journal, 1940