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Can we reconstruct a 3D object from 2D<br />
• Tuy 1983, Kirillow 1961<br />
• condition for trajectory to facilitate exact<br />
reconstruction from cone-beam projections<br />
• Feldkamp <strong>et</strong> <strong>al</strong>., 1984<br />
• extension of 2D filtered backprojection with<br />
circle trajectory to 3D (cone-beam)<br />
• works well in many practic<strong>al</strong> applications<br />
• artefacts for high cone-angle<br />
• Danielsson <strong>et</strong> <strong>al</strong>., 1997<br />
• Each object point lies on a unique PI-line<br />
(helix trajectory)<br />
X-ray projections?<br />
“ ... To accurately reconstruct an image for a ROI, <strong>al</strong>l the<br />
planes passing through the ROI should intersect the<br />
source trajectory at least once in a nontangenti<strong>al</strong> and<br />
nonended way. ... “<br />
Tuy, “An inverse formula for cone-beam reconstruction,” SIAM J Appl. Math., 1983.
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