Author/Authors :
Maltseva, S.V. Sobolev Institute of Mathematics, Novosibirsk, Russia , Svetov, I.E. Sobolev Institute of Mathematics, Novosibirsk, Russia , Polyakova, A.P. Sobolev Institute of Mathematics, 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 , Rie- mannian metric , singular support
