Computer simulations for the effectiveness of CT image reconstruction using hexagonal grids versus the usual square grids with the same sampling rate

The usual CT image reconstruction is on the square lattice (sqL). However, it has been shown that the hexagonal lattice (hexL) gives the highest density circle packing among all lattices in the two-dimensional Euclidean plane. Hence, when an image is sampled by both the sqL and hexL under the same sampling rate, the hexagonally sampled image has better correlation to the projected data (from CT scans) than the image sampled by the sqL. In this paper, we perform computer simulations for CT image reconstructions using filtered backprojection methods on the hexL versus sqL. Both the parallel beam and fanbeam projections are considered. For the fanbeam projections, both the formular and rebinning methods are examined. We also show the effectiveness of the hexL versus sqL for CT image reconstructions based on some usual image dissimilarity measures between the two reconstructed images and the two originally discretized images correspondingly. The output data show that hexL is more effective than the corresponding sqL. The reconstructed images and data from those algorithms are displayed for convenient comparisons. Furthermore, the subsampling effect of Radon transforms for those two different kinds of lattices is displayed to show the corresponding effect of the distribution of lattice points in the 2D region for CT image reconstruction.