Tomographic reconstruction using 3D deformable models

We address the issue of reconstructing the shape of an object with uniform interior activity from a set of projections. We estimate directly from projection data the position of a triangulated surface describing the boundary of the object while incorporating prior knowledge about the unknown shape. This inverse problem is addressed in a Bayesian framework using the maximum a posteriori (MAP) estimate for the reconstruction. The derivatives needed for the gradient-based optimization of the model parameters are obtained using the adjoint differentiation technique. We present results from a numerical simulation of a dynamic cardiac imaging study. A first-pass exam is simulated with a numerical phantom of the right ventricle using the measured system response of the University of Arizona FASTSPECT imager, which consists of 24 detectors. We demonstrate the usefulness of our approach by reconstructing the shape of the ventricle from 10 000 counts. The comparison with an ML-EM result shows the usefulness of the deformable model approach.