Compton camera imaging and Radon transforms on the cone: From data to images
Résumé
The recent advances in Compton camera imaging led to new integral transforms that may be assimilated to Radon transforms on cones. We mainly have two classes of models. The first one consists in integrating the intensity function on the cone’s surface and in the second one the activity measured on the set of generatrices is summed. The inverse transform either gives directly the unknown intensity function or its integrals on half-lines. For the first approach some filtered back-projection algorithms were proposed. The second approach is well adapted for far-field imaging and for mono-pixel scatterers.
In this work the emphasis will be put on planar acquisition geometries. First, a brief discussion of the models usually employed in Compton camera imaging will be carried, with the support of theoretical arguments and Monte-Carlo simulation results. Then a filtered back-projection algorithm will be presented. Finally, the influence of the model on the reconstructed images will be shown.