# Eigenvalue and Eigenvector Expansions for Image Reconstruction

### Tomohiro Aoyagi, Kouichi Ohtsubo

#### 2022

#### Abstract

In medical imaging modality, such as X-ray computerized tomography, image reconstruction from projection is to produce the density distribution within the human body from estimates of its line integrals along a finite number of lines of known locations. Generalized Analytic Reconstruction from Discrete Samples (GARDS) can be derived by the Singular Value Decomposition analysis. In this paper, by discretizing the image reconstruction problem, we applied GARDS to the problem and evaluated the image quality. We have computed the condition number in the case of changing the views and the normalized mean square error in the case of changing the views and the number of the eigenvectors. We have showed that the error decreases with increasing the number of eigenvectors and the number of views.

Download#### Paper Citation

#### in Harvard Style

Aoyagi T. and Ohtsubo K. (2022). **Eigenvalue and Eigenvector Expansions for Image Reconstruction**. In *Proceedings of the 10th International Conference on Photonics, Optics and Laser Technology - Volume 1: PHOTOPTICS,* ISBN 978-989-758-554-8, pages 111-115. DOI: 10.5220/0010807900003121

#### in Bibtex Style

@conference{photoptics22,

author={Tomohiro Aoyagi and Kouichi Ohtsubo},

title={Eigenvalue and Eigenvector Expansions for Image Reconstruction},

booktitle={Proceedings of the 10th International Conference on Photonics, Optics and Laser Technology - Volume 1: PHOTOPTICS,},

year={2022},

pages={111-115},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0010807900003121},

isbn={978-989-758-554-8},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 10th International Conference on Photonics, Optics and Laser Technology - Volume 1: PHOTOPTICS,

TI - Eigenvalue and Eigenvector Expansions for Image Reconstruction

SN - 978-989-758-554-8

AU - Aoyagi T.

AU - Ohtsubo K.

PY - 2022

SP - 111

EP - 115

DO - 10.5220/0010807900003121