A new formula of the Radon transform inversion

Author

Kazantsev, I.G.

Author_Institution

Image Process. Group, Comput. Center, Novosibirsk, Russia

Volume

1

fYear

1997

fDate

26-29 Oct 1997

Firstpage

189

Abstract

In this paper the well-known Radon transform inversion problem is considered. An approach to optimal reconstruction from a finite number of arbitrary directed projections within the framework of the conventional parallel beam geometry is suggested. The method considered converges to the minimal solution of the Radon problem, and a linear system of the Fredholm integral equations of the third kind in terms of one-dimensional functions is derived. As a consequence of the approach a new formula of the Radon transform inversion and a functional determining projection information content are obtained. The results of computer modelling are presented

Keywords

Fredholm integral equations; Radon transforms; computerised tomography; functional equations; image reconstruction; inverse problems; Fredholm integral equations; Radon transform inversion; arbitrary directed projections; computer modelling; computerised tomography; convergence; functional; image reconstruction; one-dimensional functions; optimal reconstruction; parallel beam geometry; projection information content; Computed tomography; Geometry; Image converters; Image processing; Image reconstruction; Integral equations; Linear systems; Matrix decomposition; Polynomials; Transforms;

fLanguage

English

Publisher

ieee

Conference_Titel

Image Processing, 1997. Proceedings., International Conference on

Conference_Location

Santa Barbara, CA

Print_ISBN

0-8186-8183-7

Type

conf

DOI

10.1109/ICIP.1997.647443

Filename

647443