Title
Stability estimates for helical computer tomography
Abbreviated Journal Title
J. Fourier Anal. Appl.
Keywords
cone-beam; helical tomography; inversion; extension to distributions; stability estimates; Sobolev spaces; microlocal analysis; X-RAY TRANSFORM; CONE-BEAM TOMOGRAPHY; RADON TRANSFORMS; RECONSTRUCTION; ALGORITHM; Mathematics, Applied
Abstract
In this article we analyze an inversion formula for helical computer tomography proposed earlier by the author. Our first result is a global stability estimate. The formula is continuous of order I in the Sobolev norms. Then the formula is extended to distributions. Originally it was derived only for C-0(infinity) functions. It turns out that there exist distributions, to which the formula does not apply. These exceptional distributions are characterized in terms of their wave fronts. Finally, we show that microlocally away from a critical set the continuity estimate can be improved: The order goes down from 1 to 1/2.
Journal Title
Journal of Fourier Analysis and Applications
Volume
11
Issue/Number
1
Publication Date
1-1-2005
Document Type
Article
Language
English
First Page
85
Last Page
105
WOS Identifier
ISSN
1069-5869
Recommended Citation
"Stability estimates for helical computer tomography" (2005). Faculty Bibliography 2000s. 5328.
https://stars.library.ucf.edu/facultybib2000/5328
Comments
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