Title

Interior Tomography With Continuous Singular Value Decomposition

Authors

Authors

X. Jin; A. Katsevich; H. Y. Yu; G. Wang; L. Li;Z. Q. Chen

Comments

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Abbreviated Journal Title

IEEE Trans. Med. Imaging

Keywords

Hilbert transform; interior tomography; singular value decomposition; (SVD); X-ray computed tomography (CT); TRUNCATED HILBERT TRANSFORM; IMAGE-RECONSTRUCTION; LOCAL TOMOGRAPHY; Computer Science, Interdisciplinary Applications; Engineering, ; Biomedical; Engineering, Electrical & Electronic; Imaging Science &; Photographic Technology; Radiology, Nuclear Medicine & Medical Imaging

Abstract

The long-standing interior problem has important mathematical and practical implications. The recently developed interior tomography methods have produced encouraging results. A particular scenario for theoretically exact interior reconstruction from truncated projections is that there is a known subregion in the region of interest (ROI). In this paper, we improve a novel continuous singular value decomposition (SVD) method for interior reconstruction assuming a known subregion. First, two sets of orthogonal eigen-functions are calculated for the Hilbert and image spaces respectively. Then, after the interior Hilbert data are calculated from projection data through the ROI, they are projected onto the eigen-functions in the Hilbert space, and an interior image is recovered by a linear combination of the eigen-functions with the resulting coefficients. Finally, the interior image is compensated for the ambiguity due to the null space utilizing the prior subregion knowledge. Experiments with simulated and real data demonstrate the advantages of our approach relative to the projection onto convex set type interior reconstructions.

Journal Title

Ieee Transactions on Medical Imaging

Volume

31

Issue/Number

11

Publication Date

1-1-2012

Document Type

Article

Language

English

First Page

2108

Last Page

2119

WOS Identifier

WOS:000313689400010

ISSN

0278-0062

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