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10 February 2009 Reversible integer 2D Fourier transform
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Proceedings Volume 7245, Image Processing: Algorithms and Systems VII; 724503 (2009)
Event: IS&T/SPIE Electronic Imaging, 2009, San Jose, California, United States
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.
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Elias Gonzalez and Artyom M. Grigoryan "Reversible integer 2D Fourier transform", Proc. SPIE 7245, Image Processing: Algorithms and Systems VII, 724503 (10 February 2009);

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