Title

Singular value decomposition for the truncated Hilbert transform

Authors

Authors

A. Katsevich

Comments

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Abbreviated Journal Title

Inverse Probl.

Keywords

CONE-BEAM CT; IMAGE-RECONSTRUCTION; RADON-TRANSFORM; Mathematics, Applied; Physics, Mathematical

Abstract

Starting from a breakthrough result by Gelfand and Graev, inversion of the Hilbert transform became a very important tool for image reconstruction in tomography. In particular, their result is useful when the tomographic data are truncated and one deals with an interior problem. As was established recently, the interior problem admits a stable and unique solution when some a priori information about the object being scanned is available. The most common approach to solving the interior problem is based on converting it to the Hilbert transform and performing analytic continuation. Depending on what type of tomographic data are available, one gets different Hilbert inversion problems. In this paper, we consider two such problems and establish singular value decomposition for the operators involved. We also propose algorithms for performing analytic continuation.

Journal Title

Inverse Problems

Volume

26

Issue/Number

11

Publication Date

1-1-2010

Document Type

Article

Language

English

First Page

12

WOS Identifier

WOS:000283054000011

ISSN

0266-5611

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