1. FBP algorithms for attenuated fan-beam projections
- Author
-
Jiangsheng You, Zhengrong Liang, and Gengsheng L. Zeng
- Subjects
Physics ,Applied Mathematics ,Probleme inverse ,Attenuation ,Data reconstruction ,Detector ,Physics::Medical Physics ,Reconstruction algorithm ,Inverse problem ,Article ,Object detection ,law.invention ,Computer Science Applications ,Theoretical Computer Science ,Filtered backprojection ,law ,Signal Processing ,Partial derivative ,Physics::Accelerator Physics ,Cartesian coordinate system ,Polar coordinate system ,Algorithm ,Mathematical Physics ,Mathematics - Abstract
A filtered backprojection (FBP) reconstruction algorithm for attenuated fan-beam projections has been derived based on Novikov’s inversion formula. The derivation uses a common transformation between parallel-beam and fan-beam coordinates. The filtering is shift-invariant. Numerical evaluation of the FBP algorithm is presented as well. As a special application, we also present a shift-invariant FBP algorithm for fan-beam SPECT reconstruction with uniform attenuation compensation. Several other fan-beam reconstruction algorithms are also discussed. In the attenuation-free case, our algorithm reduces to the conventional fan-beam FBP reconstruction algorithm.
- Published
- 2005