High-Quality Volumetric Reconstruction on Optimal Lattices for Computed Tomography

Within the context of emission tomography, we study volumetric reconstruction methods based on the Expectation Maximization (EM) algorithm. We show, for the first time, the equivalence of the standard implementation of the EM-based reconstruction with an implementation based on hardware-accelerated volume rendering for nearestneighbor (NN) interpolation. This equivalence suggests that higher-order kernels should be used with caution and do not necessarily lead to better performance. We also show that the EM algorithm can easily be adapted for different lattices, the body-centered cubic (BCC) one in particular. For validation purposes, we use the 3D version of the Shepp-Logan synthetic phantom, for which we derive closed-form analytical expressions of the projection data. The experimental results show the theoretically-predicted optimality of NN interpolation in combination with the EM algorithm, for both the noiseless and the noisy case. Moreover, reconstruction on the BCC lattice leads to superior accuracy, more compact data representation, and better noise reduction compared to the Cartesian one. Finally, we show the usefulness of the proposed method for optical projection tomography of a mouse embryo.