TY - JOUR
T1 - Quantitative reconstruction from truncated projections in classical tomography
AU - Clackdoyle, Rolf
AU - Noo, Frédéric
AU - Guo, Junyu
AU - Roberts, John A.
N1 - Funding Information:
Manuscript received November 16, 2003; revised July 22, 2004. This work was supported in part by the U.S. National Institutes of Health under Grants R21 CA82843, R21 EB000568, and R01 EB000627. The authors are with the Department of Radiology, University of Utah, Salt Lake City, UT 84108 USA (e-mail: [email protected]). Digital Object Identifier 10.1109/TNS.2004.835781 Fig. 1. (Left) Illustration of sinogram variables and (right) an example of a sinogram.
PY - 2004/10
Y1 - 2004/10
N2 - We prove that some kinds of truncation are entirely admissible for region-of-interest (ROI) reconstructions in classical tomography, contrary to the long-standing folklore that two-dimensional tomography is "all or nothing." The proof is based on a link between the Hubert transforms of parallel beam and fanbeam projections, which was recently used by Noo et al. to achieve ROI image reconstruction from fanbeam data on less than a short scan, assuming no fanbeam truncation occurs. We extend the use of this link to achieve quantitative ROI reconstruction in the presence of truncated projections. Our results are illustrated with a specific example of a parallel-hole detector of length 24 cm and an elliptical object of 15- and 30-cm axes. The detector rotates 180° about a point on the long axis at 11.25 cm from the right-hand-side boundary. The right half of the ellipse, the ROI in this case, is not truncated, although the left side is truncated in many views. The ROI can be quantitatively reconstructed, as is verified by our simulation. We also show that under certain conditions, ROI reconstruction is possible with truncation on both sides of the field of view. These results bring new understanding to the fondamental mechanisms of tomography. Benefits of this new understanding can be anticipated in many classical tomography applications, particularly when the projections of the object are too wide for the available detector.
AB - We prove that some kinds of truncation are entirely admissible for region-of-interest (ROI) reconstructions in classical tomography, contrary to the long-standing folklore that two-dimensional tomography is "all or nothing." The proof is based on a link between the Hubert transforms of parallel beam and fanbeam projections, which was recently used by Noo et al. to achieve ROI image reconstruction from fanbeam data on less than a short scan, assuming no fanbeam truncation occurs. We extend the use of this link to achieve quantitative ROI reconstruction in the presence of truncated projections. Our results are illustrated with a specific example of a parallel-hole detector of length 24 cm and an elliptical object of 15- and 30-cm axes. The detector rotates 180° about a point on the long axis at 11.25 cm from the right-hand-side boundary. The right half of the ellipse, the ROI in this case, is not truncated, although the left side is truncated in many views. The ROI can be quantitatively reconstructed, as is verified by our simulation. We also show that under certain conditions, ROI reconstruction is possible with truncation on both sides of the field of view. These results bring new understanding to the fondamental mechanisms of tomography. Benefits of this new understanding can be anticipated in many classical tomography applications, particularly when the projections of the object are too wide for the available detector.
KW - Reconstruction
KW - Tomography
KW - Truncated data
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U2 - 10.1109/TNS.2004.835781
DO - 10.1109/TNS.2004.835781
M3 - Article
AN - SCOPUS:4043157202
SN - 0018-9499
VL - 51
SP - 2570
EP - 2578
JO - IEEE Transactions on Nuclear Science
JF - IEEE Transactions on Nuclear Science
IS - 5 II
ER -