Stability estimates for helical computer tomography
Abbreviated Journal Title
J. Fourier Anal. Appl.
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
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 of Fourier Analysis and Applications
"Stability estimates for helical computer tomography" (2005). Faculty Bibliography 2000s. 5328.