Title

Stability Estimates For Helical Computer Tomography

Keywords

Cone-beam; Extension to distributions; Helical tomography; Inversion; Microlocal analysis; Sobolev spaces; Stability estimates

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 1 in the Sobolev norms. Then the formula is extended to distributions. Originally it was derived only for C0∞ 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.

Publication Date

2-1-2005

Publication Title

Journal of Fourier Analysis and Applications

Volume

11

Issue

1

Number of Pages

85-105

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s00041-004-4013-6

Socpus ID

13844296436 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/13844296436

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