Radon Transform and Tomographic Reconstruction of Time- Dependent Circles and Ellipses

C. C. Dantasa, S. B. Melob, E. A. O. Limac

aDepartamento de Engenharia Nuclear da Universidade Federal de Pernambuco, Recife-PE,Brazil

bCentro de Informática da Universidade Federal de Pernambuco, Recife-PE, Brazil

cEscola Politécnica da Universidade de Pernambuco, Recife-PE, Brazil

Abstract

The two-dimensional Radon transform is the line integral of a function of the plane calculated along straight paths in this plane. The mathematical techniques needed to compute these transforms and their inverses were developed by J. Radon in 1917 [1] and nowadays are applied to such different areas as the processing of geo-seismic information and the CT medical imaging [2]. Although these techniques are well established, and computationally feasible algorithms available, the practical problem of producing a two-variable function out of a sampling of their Radon transforms, known as the problem of tomography reconstruction, is still subject of intense research, particularly in applications where a limited number of such samples is available [3]. A restricted version of this problem is the production of tomographic reconstruction of functions defined in a region of the plane - called tomographic profiles - which vary over the sampling time, what is called dynamic tomography [4,5]. In this paper, we study the problem of dynamic topography reconstruction of analytical models, i.e., circles and ellipses, whose shape and positioning parameters vary according to schemes known over time. By means of analytical model evaluation of dynamic data are carried out. In spite of experimental errors and high variance in data, spatial resolution in dynamic tomography is competitive by a factor of two which might improve capturing data trend in solid flow investigation.

Keywords: Dinamic Tomography; Radon Transform; Non-Destructive Essays