Exact image representation via a number-theoretic Radon transform

Chandra, Shekhar S. and Svalbe, Imants (2014) Exact image representation via a number-theoretic Radon transform. IET Computer Vision, 8 4: 338-346. doi:10.1049/iet-cvi.2013.0101

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Author Chandra, Shekhar S.
Svalbe, Imants
Title Exact image representation via a number-theoretic Radon transform
Journal name IET Computer Vision   Check publisher's open access policy
ISSN 1751-9632
Publication date 2014-08
Year available 2014
Sub-type Article (original research)
DOI 10.1049/iet-cvi.2013.0101
Open Access Status
Volume 8
Issue 4
Start page 338
End page 346
Total pages 9
Place of publication Stevenage, Herts, United Kingdom
Publisher The Institution of Engineering and Technology
Collection year 2015
Language eng
Formatted abstract
This study presents an integer-only algorithm to exactly recover an image from its discrete projected views that can be computed with the same computational complexity as the fast Fourier transform (FFT). Most discrete transforms for image reconstruction rely on the FFT, via the Fourier slice theorem (FST), in order to compute reconstructions with low-computational complexity. Consequently, complex arithmetic and floating point representations are needed, the latter of which is susceptible to round-off errors. This study shows that the slice theorem is valid within integer fields, via modulo arithmetic, using a circulant theory of the Radon transform (RT). The resulting number-theoretic RT (NRT) provides a representation of images as discrete projections that is always exact and real-valued. The NRT is ideally suited as part of a discrete tomographic algorithm, an encryption scheme or for when numerical overflow is likely, such as when computing a large number of convolutions on the projections. The low-computational complexity of the NRT algorithm also provides an efficient method to generate discrete projected views of image data.
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: Non HERDC
School of Information Technology and Electrical Engineering Publications
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Created: Tue, 01 Jul 2014, 14:59:40 EST by Shekhar Chandra on behalf of School of Information Technol and Elec Engineering