Utilization of Cross-Plane Rays for Three-Dimensional Reconstruction by Filtered Back-Projection

Abstract

Present popular computed tomography (CT) algorithms reconstruct an object from the ray measurements lying on a set of parallel planes. This paper presents an algorithm that can also utilize "cross-plane" rays (i.e., rays that cross through many planes) to reconstruct the object. In this reconstruction algorithm, the ray measurements are grouped into two-dimensional projections, filtered, and stored. The filtered projections can then be back-projected onto a three-dimensional matrix or any plane through the three-dimensional volume. General theoretical aspects are presented and then applied to the special case in which ray measurements have been made in all directions. The algorithm is tested using computer-generated data. Expressions for the noise power spectrum and the variance in the reconstruction are derived. It is shown that the noise-to-signal ratio per detected photon for this reconstruction method is close to a theoretical limit, as it also is for normal CT. The ability to use ray measurements that cross many planes is especially useful in emission CT, where order-of-magnitude improvements in image quality per unit dose can be achieved.