This article is cited in 1 paper

Reconstruction of a function and its singular support in a cylinder by tomographic data

S. V. Mal'tseva, I. E. Svetov, A. P. Polyakova

Sobolev Institute of Mathematics, 630090 Novosibirsk, Russia

Abstract: In this article we consider problems of reconstruction of a function and its singular support by using tomographic data. The data for the problems are values of the attenuated geodesic x-ray transform which is a set of integrals of an unknown function calculated along geodesics of the Riemannian metric that is used for modelling refraction in a cylinder. The values of the attenuated geodesic x-ray transform are received in a slice-by-slice fan-beam scheme. Our approach is based on the slice-by-slice reconstruction of the sought-for function or its singular support using a modification of well-known operators of back-projection and break indicator.

Keywords: Tomography, refraction, absorption, attenuated geodesic x-ray transform, Riemannian metric, singular support.

MSC: 65R10, 65R32

Language: English

DOI: 10.32523/2306-6172-2020-8-2-86-97

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