Three-dimensional attenuation map reconstruction using geometrical models and free-form deformations [SPECT application]

Addresses the issue of using deformable models to reconstruct an unknown attenuation map of the torso from a set of transmission scans. The authors assume the three-dimensional (3-D) distribution of attenuation coefficients to be piecewise uniform. They represent the unknown distribution by a set of closed surfaces defining regions having the same attenuating properties. The methods of reconstruction published so far tend to directly deform the surfaces, the parameters being the surface elements. Rather than deforming the surfaces, the authors explore the possibility of deforming the space in which the geometrical primitives are contained. They focus on the use of free-form deformations (FFD's) to describe the continuous transformation of space used to match a set of transmission measurements. They illustrate this approach by reconstructing realistically simulated transmission scans of the torso with various noise levels and compare the results to standard reconstruction methods.