A fast number theoretic finite radon transform

Chandra, S. and Svalbe, I. (2009). A fast number theoretic finite radon transform. In: Hao Shi, DICTA 2009 : 2009 digital image computing techniques and applications : proceedings. Digital Image Computing: Techniques and Applications, DICTA 2009, Melbourne, VIC Australia, (361-368). 1 - 3 December 2009. doi:10.1109/DICTA.2009.67

Author Chandra, S.
Svalbe, I.
Title of paper A fast number theoretic finite radon transform
Conference name Digital Image Computing: Techniques and Applications, DICTA 2009
Conference location Melbourne, VIC Australia
Conference dates 1 - 3 December 2009
Proceedings title DICTA 2009 : 2009 digital image computing techniques and applications : proceedings
Place of Publication Piscataway, NJ United States
Publisher I E E E
Publication Year 2009
Year available 2009
Sub-type Fully published paper
DOI 10.1109/DICTA.2009.67
Open Access Status
ISBN 9780769538662
Editor Hao Shi
Start page 361
End page 368
Total pages 8
Language eng
Abstract/Summary This paper presents a new fast method to map between images and their digital projections based on the Number Theoretic Transform (NTT) and the Finite Radon Transform (FRT). The FRT is a Discrete Radon Transform (DRT) defined on the same finite geometry as the Finite or Discrete Fourier Transform (DFT). Consequently, it may be inverted directly and exactly via the Fast Fourier Transform (FFT) without any interpolation or filtering [1]. As with the FFT, the FRT can be adapted to square images of arbitrary sizes such as dyadic images, prime-adic images and arbitrary-sized images. However, its simplest form is that of prime-sized images [2]. The FRT also preserves the discrete versions of both the Fourier Slice Theorem (FST) and Convolution Property of the Radon Transform (RT). The NTT is also defined on the same geometry as the DFT and preserves the Circular Convolution Property (CCP) of the DFT [3, 4]. This paper shows that the Slice Theorem is also valid within the NTT and that it can be utilized as a new exact, integer-only and fast inversion scheme for the FRT, with the same computational complexity as the FFT. Digital convolutions and exact digital filtering of projections can also be performed using this Number Theoretic FRT (NFRT).
Subjects 1703 Computational Theory and Mathematics
1704 Computer Graphics and Computer-Aided Design
1712 Software
Keyword Discrete radon transforms
Discrete tomography
Fast fourier transform
Finite fields
Number theoretic transform
Q-Index Code E1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Conference Paper
Sub-type: Fully published paper
Collection: School of Information Technology and Electrical Engineering Publications
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Created: Wed, 19 Mar 2014, 21:08:38 EST by Shekhar Chandra on behalf of School of Information Technol and Elec Engineering