Abstract
In order to perform fan-beam reconstruction using projection data collected from a noncircular scanning locus, existing noncircular fan-beam formulas require a derivative of the scanning locus with respect to the rotation angle. In this paper, a derivative-free noncircular fan-beam reconstruction formula is obtained based on a geometrical explanation of the circular equispatial fan-beam reconstruction formula. A mathematical proof is then provided under the conditions that the source-to-origin distance is symmetric with respect to the origin of the reconstruction coordinate system, is differentiable almost everywhere and changes not too fast with respect to the rotation angle. The derivative-free noncircular fan-beam reconstruction formula is the same as the circular one, except that the source-to-origin distance is a function of the rotation angle. A typical simulation result of the noncircular fan-beam formula is given.
| Original language | English |
|---|---|
| Pages (from-to) | 543-547 |
| Number of pages | 5 |
| Journal | IEEE Transactions on Image Processing |
| Volume | 2 |
| Issue number | 4 |
| DOIs | |
| State | Published - Oct 1993 |
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