Title

Cone beam local tomography

Authors

Authors

A. Katsevich

Comments

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Abbreviated Journal Title

SIAM J. Appl. Math.

Keywords

spiral CT; cone-beam data; local tomography; pseudodifferential; operators; singularities; artifacts; X-RAY TRANSFORM; SUFFICIENT CONDITIONS; RECONSTRUCTION; ALGORITHM; Mathematics, Applied

Abstract

In this paper we study three-dimensional cone beam local tomography. We analyze the local tomography function f(Lambda)(c), which was proposed earlier in [A.K. Louis and P. Maass, IEEE Trans. Medical Imaging, 12 (1993), pp. 764-769]. Let f be an unknown density distribution inside an object being scanned. We find a relationship between the wave fronts of f(Lambda)(c) and f and compute the principal symbol of the operator which maps f into f(Lambda)(c). Our results prove the fact, which was first noted in Louis and Maass, that one can recover most of the singularities of f knowing f(Lambda)(c). It is shown that these are precisely the singularities of f that are visible from the data. A simple and efficient algorithm for finding values of jumps of f knowing local cone beam data is proposed. The nature of artifacts inherent in cone beam local tomography is studied.

Journal Title

Siam Journal on Applied Mathematics

Volume

59

Issue/Number

6

Publication Date

1-1-1999

Document Type

Article

Language

English

First Page

2224

Last Page

2246

WOS Identifier

WOS:000083607800013

ISSN

0036-1399

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