16 March 2015 Tensor representation of color images and fast 2D quaternion discrete Fourier transform
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In this paper, a general, efficient, split algorithm to compute the two-dimensional quaternion discrete Fourier transform (2-D QDFT), by using the special partitioning in the frequency domain, is introduced. The partition determines an effective transformation, or color image representation in the form of 1-D quaternion signals which allow for splitting the N × M-point 2-D QDFT into a set of 1-D QDFTs. Comparative estimates revealing the efficiency of the proposed algorithms with respect to the known ones are given. In particular, a proposed method of calculating the 2r × 2r -point 2-D QDFT uses 18N2 less multiplications than the well-known column-row method and method of calculation based on the symplectic decomposition. The proposed algorithm is simple to apply and design, which makes it very practical in color image processing in the frequency domain.
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Artyom M. Grigoryan, Artyom M. Grigoryan, Sos S. Agaian, Sos S. Agaian, "Tensor representation of color images and fast 2D quaternion discrete Fourier transform", Proc. SPIE 9399, Image Processing: Algorithms and Systems XIII, 93990N (16 March 2015); doi: 10.1117/12.2083199; https://doi.org/10.1117/12.2083199

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