A simple method for tomography reconstruction

Abstract

The problem of reconstructing an image from projections has been extensively 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 co-efficents need to be considered in the reconstruction process. In this work, we present an alternative tomography reconstruction method based on the sensitivity of an objective function with respect to small perturbations in the material properties of the problem domain. In particular, we use a simple tomography model to represent the attenuation of 1D projections through 2D slices. Then, we compute the sensitivity associated to the misfit between a boundary measurement and the model solution. Finally, we use this information to devise an iterative algorithm, which allows to reconstruct the attenuation co-efficent defined in the whole domain from exact or noisy synthetic boundary data.

Keywords:

• image projection
• tomography reconstruction
• shape sensitivity

Acknowledgements

This research was partly supported by the Brazilian agencies CNPq/FAPERJ-PRONEX, under Grant E-26/171.199/2003. I. Larrabide was partly supported by the Brazilian agency CNPq (141336/2003-0). The support of these agencies is greatly appreciated.