# Implementation of Tomographic Reconstruction on CC, BCC, and FCC Lattices

OData: XML JSON What's this?In the medical image diagnostic and three dimensional imaging it is overly preferred to represent the data as discrete samples on a simple Cartesian cubic lattice or on a rectilinear lattice. It is a logical choice in the sense that these lattices are quite easy to handle and suit well to the memory structure of computers. Furthermore the computations on them are extremely fast and simple owing to their separability which is utilized by modern GPU architectures (e.g., hardware trilinear interpolation).

Aside from all these advantages the use of Cartesian cubic lattice has several not negligable shortcomings. The sampling on these lattices is rather anisotropic, that is, the reconstruction engenders conspicuous axis aligned artifacts. Moreover the quality of the reconstructed signal is not optimal

at all. Therefore it would be favourable to apply other structures that can afford better sampling capabilities and much more isotropic reconstruction at the same density of lattice points. The best competitor is the body-centered cubic lattice which is optimal for sampling in 3D. In sampling of a spherically band-limited signal, an impovement of ~29.3% can be achieved when using the BCC lattice instead of the simple CC lattice. It means that the number of necessary lattice points for a given quality is ~29.3% less. The beneficial outcome is a far lower demand for bandwidth since the size of data to be moved and stored is much smaller. Additionally the number of steps needed by some relevant algorithms can be definitely reduced. Nevertheless, continuous reconstruction is of crucial importance to be able to utilize the advantageous properties of the BCC lattice in practice as well. It aims to build a continuous model from the dicrete representation of the signal by means of the application of a continuous reconstruction filter. It is clearly apparent that the quality of the resulting model is a product of the cooperation of both the lattice and the adapted filter kernel, thus it is not sufficient to examine their behavior separately.

Within the scope of this thesis, we investigate the question of how efficiently a pair of lattice and filter can contribute to a good quality, isotropic model. For the research we developed a software which serves a simple and effective interface for running extensive test cases. It takes advantage of the compute capacity of modern graphics processing units and of the recent technologies. Beyond the analysis of the test results, our aspiration was to give a theoretical explanation for the observed phenomena.