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An alternative proof of Bukhgeim and Kazantsev's inversion formula for attenuated fan‐beam projections
Author(s) -
Huang Qiu,
Zeng Gengsheng L.,
Wu Jiansheng
Publication year - 2006
Publication title -
medical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.473
H-Index - 180
eISSN - 2473-4209
pISSN - 0094-2405
DOI - 10.1118/1.2356649
Subject(s) - inversion (geology) , mathematics , beam (structure) , novikov self consistency principle , optics , physics , geology , pure mathematics , paleontology , structural basin
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.