Tomographic Reconstruction on the Body-Centered Cubic Lattice

It is well known that the sampling efficiency of the Body-Centered Cubic (BCC) lattice is almost 30% higher than that of the traditional Cartesian Cubic (CC) lattice. Nevertheless, the CC lattice is still a de facto standard in tomographic reconstruction. In this paper, we analyze the classical Algebraic Reconstruction Technique (ART) implemented on CC and BCC lattices using linear reconstruction kernels. We test the nonseparable linear box-spline kernel on the BCC lattice and the separable trilinear B-spline kernel on both CC and BCC lattices. Although theoretically all these kernels guarantee a first-order approximation, we show that the trilinear B-spline kernel applied on the BCC lattice results in not just the lowest residual error but the highest visual quality as well.