Computed Tomography from X-rays: Old 2-d Results, New 3-d Problems

We consider old results on 2-D computerized tomography methods and their relevance to new fully 3-D problems. We examine the 2-D filtered back-projection method (FBP)from several perspectives to better understand how it works. Based on that understanding, we question whether stable, reliable reconstruction algorithms can be found for widedetector cone-beam 3-D machines with their resulting large-slant beams. We use a numerical method of “point response function fitting” to compute convolution kernels H(u, v) (for use with back-projection) for a model slant-beam problem. These kernels exhibit disturbing growing and spreading oscillations which would greatly amplify errors in the projection data.