A Geometrical Algorithm for Inverse Reconstruction Tomographycal Image

Francisco Pablo Ramírez-García & Paola Fuentes-Morales

Depto. de Física, Facultad de Ciencias, UNAM, Circuito Exterior S/N, Ciudad Universitaria, Delg.

Coyoacán, México, D.F. 04510, MEXICO, fcopabloramirez@ciencias.unam.mx

ABSTRACT

It is presented an algorithm for obtaining the reconstructed tomogram using linear algebra that is based in a geometrical array of the sources and the detectors. This algorithm constructs a matrix of the lengths of the rays that cruces each pixel that allows to use the normal least squares method to obtain the mean attenuation coefficient of each pixel, since the matrix in the normal equation is not singular or ill conditioned.

The geometrical array corresponds to positioning the sources and detectors in a circle, the sources are located at each vertex of an irregular polygon and the detectors are equally displaced over the opposite side of the circle, in a way that covers the complete object to analyze.

Keywords Inverse Reconstruction, Normal equation, Geometrical Tomography Procedure, Direct Algebraic Reconstruction Tomography, Industrial Tomography