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Tomographic Inverse Problem with Estimating Missing Projections
Joint Authors
Yamaguchi, Yusaku
Kimura, Masashi
Yoshinaga, Tetsuya
Abou Al-Ola, Omar M.
Source
Mathematical Problems in Engineering
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-03-13
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
Image reconstruction in computed tomography can be treated as an inverse problem, namely, obtaining pixel values of a tomographic image from measured projections.
However, a seriously degraded image with artifacts is produced when a certain part of the projections is inaccurate or missing.
A novel method for simultaneously obtaining a reconstructed image and an estimated projection by solving an initial-value problem of differential equations is proposed.
A system of differential equations is constructed on the basis of optimizing a cost function of unknown variables for an image and a projection.
Three systems described by nonlinear differential equations are constructed, and the stability of a set of equilibria corresponding to an optimized solution for each system is proved by using the Lyapunov stability theorem.
To validate the theoretical result given by the proposed method, metal artifact reduction was numerically performed.
American Psychological Association (APA)
Kimura, Masashi& Yamaguchi, Yusaku& Abou Al-Ola, Omar M.& Yoshinaga, Tetsuya. 2019. Tomographic Inverse Problem with Estimating Missing Projections. Mathematical Problems in Engineering،Vol. 2019, no. 2019, pp.1-11.
https://search.emarefa.net/detail/BIM-1197240
Modern Language Association (MLA)
Kimura, Masashi…[et al.]. Tomographic Inverse Problem with Estimating Missing Projections. Mathematical Problems in Engineering No. 2019 (2019), pp.1-11.
https://search.emarefa.net/detail/BIM-1197240
American Medical Association (AMA)
Kimura, Masashi& Yamaguchi, Yusaku& Abou Al-Ola, Omar M.& Yoshinaga, Tetsuya. Tomographic Inverse Problem with Estimating Missing Projections. Mathematical Problems in Engineering. 2019. Vol. 2019, no. 2019, pp.1-11.
https://search.emarefa.net/detail/BIM-1197240
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1197240