An alternative proof of Bukhgeim and Kazantsev's inversion formula for attenuated fan-beam projections.
An inversion formula was developed by Bukhgeim and Kazantsev for attenuated fan-beam projections [Russian Academy of Science Siberian Branch: The Sobolev Institute of Mathematics (2002)]. The inversion formula was obtained by relating the attenuated fan-beam projections to unattenuated fan-beam projections and by trickily processing the unattenuated fan-beam projections. We show in this paper that the inversion formula can be readily obtained from Novikov's inversion formula for the two-dimensional (2D) attenuated radon transform. The derivation provides an alternative proof of Bukhgeim and Kazantsev's inversion formula by the use of transformation between parallel-beam coordinates and fan-beam coordinates and thus is quite elementary.
Huang
Qiu
Q
Utah Center for Advanced Imaging Research, University of Utah, Salt Lake City, Utah 84108, USA. qhuang@ece.utah.edu
Zeng
Gengsheng L
GL
Wu
Jiansheng
J
D000465:Algorithms; D016247:Information Storage and Retrieval / Q000379:methods; D009716:Numerical Analysis, Computer-Assisted; D011856:Radiographic Image Enhancement / Q000379:methods*; D011857:Radiographic Image Interpretation, Computer-Assisted / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D036542:Tomography, Spiral Computed / Q000379:methods*