A simple method for tomography reconstruction based on a discrete version of the topological gradient.

I. LARRABIDE; A. A. NOVOTNY; R. A. FEIJÓO

Miami

Simposio; Inverse Problems, Design and Optimization Symposium 2007 (IPDO-2007),; 2007

Universidade Federal de Rio de Janeiro

The problem of reconstructing an image from projections has been largely studied. Nowadays, the so called ”Direct methods” (based on Fourier transform) are the most widely used, mainly because of its low computational cost. Nevertheless, in some situations old fashion iterative algorithms are more appropriate as is the case of Nuclear imaging, where attenuation coefficients need to be considered in the reconstruction process. In this work we present a reconstruction method based on the well established concept of topological sensitivity analysis for a simple tomography model. This concept is based on analyzing the sensitivity of a cost function to small perturbations in the domain topology or material properties. In particular, the tomography model is used to reconstruct the attenuation coefficient from 1D projections thought 2D slices. After revisiting the topological expansion concept and presenting the cost function under consideration, the topological gradient is computed. In the results section the topological gradient information is used to devise an iterative reconstruction algorithm and finally, some results are shown.