Abstract
Abstract
The operators of longitudinal, transverse and mixed ray transforms acting on two-dimensional symmetric tensor fields of arbitrary degree m in an unit disk are considered in the article. The singular value decompositions of the operators for a parallel scheme of data acquisition are constructed. Orthogonal bases in original spaces and image spaces are constructed using harmonic, Jacobi and Gegenbauer polynomials. Based on the obtained decompositions the polynomial expressions for the (pseudo)inverse and adjoint operators are obtained.
Funder
the government assignment of the Sobolev Institute of Mathematics
Subject
Applied Mathematics,Computer Science Applications,Mathematical Physics,Signal Processing,Theoretical Computer Science
Reference51 articles.
1. Optical tomography of stress tensor field;Aben,1991
2. The attenuated magnetic ray transform on surfaces;Ainsworth;Inverse Problems Imaging,2013
3. Stability estimates in tensor tomography;Boman;Inverse Problems Imaging,2018
4. Tomographic reconstruction of vector fields;Braun;IEEE Trans. Signal Process.,1991
5. A singular value decomposition for the Radon transform in n-dimen-sional Euclidean space;Davison;Numer. Funct. Anal. Optimiz.,1981
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