Computed tomography from X-rays: Old 2-D results, new 3-D problems

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.

Keywords:

• Computerized tomography
• Fully 3-D reconstruction
• Filtered back-projection
• Cone-beam CT

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.