Title :
A new formula of the Radon transform inversion
Author_Institution :
Image Process. Group, Comput. Center, Novosibirsk, Russia
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;
Conference_Titel :
Image Processing, 1997. Proceedings., International Conference on
Conference_Location :
Santa Barbara, CA
Print_ISBN :
0-8186-8183-7
DOI :
10.1109/ICIP.1997.647443
