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Proceedings Paper

Reversible integer 2D Fourier transform
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Paper Abstract

This paper describes the 2-D reversible integer discrete Fourier transform (RiDFT), which is based on the concept of the paired representation of the 2-D signal or image. The Fourier transform is split into a minimum set of short transforms. By means of the paired transform, the 2-D signal is represented as a set of 1-D signals which carry the spectral information of the signal at disjoint sets of frequency-points. The paired transform-based 2-D DFT involves a few operations of multiplication that can be approximated by integer transforms. Such one-point transforms with one control bit are applied for calculating the 2-D DFT. 24 real multiplications and 24 control bits are required to perform the 8x8-point RiDFT, and 264 real multiplications and 168 control bits for the 16 x 16-point 2-D RiDFT of real inputs. The computational complexity of the proposed 2-D RiDFTs is comparative with the complexity of the fast 2-D DFT.

Paper Details

Date Published: 11 February 2009
PDF: 12 pages
Proc. SPIE 7245, Image Processing: Algorithms and Systems VII, 724503 (11 February 2009); doi: 10.1117/12.804779
Show Author Affiliations
Elias Gonzalez, The Univ. of Texas at San Antonio (United States)
Artyom M. Grigoryan, The Univ. of Texas at San Antonio (United States)

Published in SPIE Proceedings Vol. 7245:
Image Processing: Algorithms and Systems VII
Nasser M. Nasrabadi; Syed A. Rizvi; Jaakko T. Astola; Karen O. Egiazarian, Editor(s)

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