A Scanning and Sampling Scheme for Computationally Efficient Algorithms of Computer Tomography

This paper presents a scanning and sampling scheme for computerized tomography that reduces the number of required interpolations in the reconstruction algorithm. Hence, the computational load associated with interpolation is also reduced. For the case where no restrictions 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. A discussion is presented on the choice of an optimal set of projection angles that will maintain an image quality comparable to a sampling scheme of regular measurement geometry, while minimizing the computational load. The Cartesian-grid scanning and sampling (CGSS) scheme developed here 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.