A scanning and sampling scheme for computationally efficient algorithms of computer tomography

A scanning and sampling scheme for computerized tomography that reduces the number of required interpolations in the reconstruction algorithm is presented. Hence, the computational load associated with interpolation is also reduced. For the case in which no restriction are placed on the sampling rates of the scanner, a set of projection angles along with their corresponding sampling rates are derived such that no interpolation is required to calculate the final image points for the display grid. From this result a reduced interpolation scheme is developed for the case when upper and lower bounds exist on the sampling rates. The choice of an optimal set of projection that will maintain an image quality comparable to a sampling scheme of regular measurement geometry, while minimizing the computational load is discussed. The Cartesian-grid scanning and sampling (CGSS) scheme developed is compared to a sampling scheme of regular measurement geometry through a computer simulation. The results demonstrate that for higher sampling rates and images of limited pixel dimension, the CGSS scheme can reduce the computational load of the reconstruction process and maintain comparable image quality