Robust digital image reconstruction via the discrete Fourier slice theorem

Chandra, Shekhar S., Normand, Nicolas, Kingston, Andrew, Guedon, Jeanpierre and Svalbe, Imants (2014) Robust digital image reconstruction via the discrete Fourier slice theorem. IEEE Signal Processing Letters, 21 6: 682-686. doi:10.1109/LSP.2014.2313341


Author Chandra, Shekhar S.
Normand, Nicolas
Kingston, Andrew
Guedon, Jeanpierre
Svalbe, Imants
Title Robust digital image reconstruction via the discrete Fourier slice theorem
Journal name IEEE Signal Processing Letters   Check publisher's open access policy
ISSN 1070-9908
1558-2361
Publication date 2014-06
Sub-type Article (original research)
DOI 10.1109/LSP.2014.2313341
Open Access Status
Volume 21
Issue 6
Start page 682
End page 686
Total pages 5
Place of publication Piscataway, NJ, United States
Publisher Institute of Electrical and Electronics Engineers
Collection year 2015
Language eng
Formatted abstract
The discrete Fourier slice theorem is an important tool for signal processing, especially in the context of the exact reconstruction of an image from its projected views. This paper presents a digital reconstruction algorithm to recover a two dimensional (2-D) image from sets of discrete one dimensional (1-D) projected views. The proposed algorithm has the same computational complexity as the 2-D fast Fourier transform and remains robust to the addition of significant levels of noise. A mapping of discrete projections is constructed to allow aperiodic projections to be converted to projections that assume periodic image boundary conditions. Each remapped projection forms a 1-D slice of the 2-D Discrete Fourier Transform (DFT) that requires no interpolation. The discrete projection angles are selected so that the set of remapped 1-D slices exactly tile the 2-D DFT space. This permits direct and mathematically exact reconstruction of the image via the inverse DFT. The reconstructions are artefact free, except for projection inconsistencies that arise from any additive and remapped noise. We also present methods to generate compact sets of rational projection angles that exactly tile the 2-D DFT space. The improvement in noise suppression that comes with the reconstruction of larger sized images needs to be balanced against the corresponding increase in computation time.
Keyword Discrete radon transform
Mojette transform
Discrete tomography
Image reconstruction
Discrete Fourier slice theorem
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: Official 2015 Collection
School of Information Technology and Electrical Engineering Publications
 
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Created: Tue, 08 Apr 2014, 13:27:47 EST by Shekhar Chandra on behalf of School of Information Technol and Elec Engineering