Analytical fan-beam and cone-beam reconstruction algorithms withuniform attenuation correction for SPECT
In this paper, we developed an analytical fan-beam reconstruction algorithm that compensates for uniform attenuation in SPECT. The new fan-beam algorithm is in the form of back projection first, then filtering, and is mathematically exact. The algorithm is based on three components. The first one is the established generalized central-slice theorem, which relates the 1D Fourier transform of a set of arbitrary data and the 2D Fourier transform of the back projected image.The second one is the fact that the back projection of the fan-beam measurements is identical to the back projection of the parallel measurements of the same object with the same attenuator. The third one is the stable analytical reconstruction algorithm for uniformly attenuated Radon data, developed by Metz and Pan. The fan-beam algorithm is then extended into a cone-beam reconstruction algorithm, where the orbit of the focal point of the cone-beam imaging geometry is a circle.This orbit geometry does not satisfy Tuy's condition and the obtained cone-beam algorithm is an approximation. In the cone-beam algorithm, the cone-beam data are first back projected into the 3D image volume; then a slice-by-slice filtering is performed. This slice-by-slice filtering procedure is identical to that of the fan-beam algorithm. Both the fan-beam and cone-beam algorithms are efficient, and computer simulations are presented. The new cone-beam algorithm is compared with Bronnikov's cone-beam algorithm, and it is shown to have better performance with noisy projections.
- Research Organization:
- Ernest Orlando Lawrence Berkeley NationalLaboratory, Berkeley, CA (US)
- Sponsoring Organization:
- USDOE Director. Office of Science. Office of Biological andEnvironmental Research. Medical Sciences Division; National Institutes ofHealth.National Institutes of Biomedical Imaging andBioengineering.National Cancer Institute Grant EB00121 and CA100181
- DOE Contract Number:
- AC02-05CH11231
- OSTI ID:
- 861025
- Report Number(s):
- LBNL--57637; BnR: 400412000
- Journal Information:
- Physics in Medicine and Biology, Journal Name: Physics in Medicine and Biology Vol. 50; ISSN 0031-9155; ISSN PHMBA7
- Country of Publication:
- United States
- Language:
- English
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