The localized basis functions for scalar and vector 3D tomography and their ray transforms

Alexander  Balandin

doi:10.3934/ipi.2016026

Article Contents

2016, Volume 10, Issue 4: 899-914. Doi: 10.3934/ipi.2016026

This issue Previous Article On the optimal control of the free boundary problems for the second order parabolic equations. II. Convergence of the method of finite differences Next Article Imaging with electromagnetic waves in terminating waveguides

The localized basis functions for scalar and vector 3D tomography and their ray transforms

Alexander Balandin^1,

1.
V.M. Matrosov Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences, Lermontov str. 134, 664033, Irkutsk-33

Received: November 30, 2015

Revised: June 30, 2016

Published: October 2016

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Abstract

Localized basis set functions related to spherical wave functions are constructed for scalar and vector 3D tomography. The functions are truncated in a spherical domain of radius $r_0$, so that these vanish outside the domain. The analytical form of the respective scalar and vector ray transforms are obtained. So, the inversion algorithm can be reduced to solving the linear system of equations because of orthogonality and completeness of the basis functions.

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Mathematics Subject Classification: 65R10, 65Z05, 65J22, 45Q05, 65R32.

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