An inversion formula for the attenuated X-ray transformation
نویسندگان
چکیده
منابع مشابه
Analytical Inversion Formula for Uniformly Attenuated Fan-Beam Projections
A convolution backprojection algorithm was derived by Tretiak and Metz to reconstruct two-dimensional (2-D) transaxial slices from uniformly attenuated parallel-beam projections. Using transformation of coordinates, this algorithm can be modified to obtain a formulation useful to reconstruct uniformly attenuated fan-beam projections. Unlike that for parallel-beam projections, this formulation d...
متن کاملAn 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 t...
متن کاملThe Attenuated X-ray Transform: Recent Developments
We survey recent work on the attenuated x-ray transform, concentrating especially on the inversion formulas found in the last few years.
متن کاملThe Identification Problem for the Attenuated X-ray Transform
We study the problem of recovery both the attenuation a and the source f in the attenuated X-ray transform in the plane. We study the linearization as well. It turns out that there is a natural Hamiltonian flow that determines which singularities we can recover. If the perturbation δa is supported in a compact set that is non-trapping for that flow, then the problem is well posed. Otherwise, it...
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ژورنال
عنوان ژورنال: Arkiv för Matematik
سال: 2002
ISSN: 0004-2080
DOI: 10.1007/bf02384507