Abstract
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 (FBP) method from several perspectives to better understand how it works. Based on that understanding, we question whether highly stable, reliable reconstruction algorithms can be found for wide-detector 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.
Acknowledgements
The author is greatly indebted to the gracious hospitality of his hosts at Oxford University Computing Laboratory, where this work was done and presented in colloquium during a sabbatical in February–March 2002.