Title

Interior Tomography With Continuous Singular Value Decomposition

Keywords

Hilbert transform; interior tomography; singular value decomposition (SVD); X-ray computed tomography (CT)

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. © 1982-2012 IEEE.

Publication Date

12-1-2012

Publication Title

IEEE Transactions on Medical Imaging

Volume

31

Issue

11

Number of Pages

2108-2119

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1109/TMI.2012.2213304

Socpus ID

84867266601 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84867266601

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