Title

Singular Value Decomposition For The Truncated Hubert Transform

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. © 2010 IOP Publishing Ltd.

Publication Date

11-9-2010

Publication Title

Inverse Problems

Volume

26

Issue

11

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1088/0266-5611/26/11/115011

Socpus ID

78049442470 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/78049442470

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