11 March 2015 Fourier transforms with rotations on circles or ellipses in signal and image processing
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Fast unitary transforms are widely used in different areas such as data compression, pattern recognition and image reconstruction, interpolation, linear filtering, and spectral analysis. In this paper, we analyze the general concept of rotation and processing of data around not only circles but ellipses, in general. For that, we describe and analyze the general concept of the elliptic Fourier transform which was developed by Grigoryan in 2009. The block-wise representation of the discrete Fourier transform is considered in the real space, which is effective and that can be generalized to obtain new methods in spectral analysis. The N-point Elliptic discrete Fourier transform (EDFT) uses as a basic 2 × 2 transformation the rotations around ellipses. The EDFT distinguishes well from the carrying frequencies of the signal in both real and imaginary parts. It also has a simple inverse matrix. It is parameterized and includes also the DFT. Our preliminary results show that by using different parameters, the EDFT can be used effectively for solving many problems in signal and image processing field, in which includes problems such as image enhancement, filtration, encryption and many others.
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Artyom M. Grigoryan, Artyom M. Grigoryan, "Fourier transforms with rotations on circles or ellipses in signal and image processing", Proc. SPIE 9411, Mobile Devices and Multimedia: Enabling Technologies, Algorithms, and Applications 2015, 94110Q (11 March 2015); doi: 10.1117/12.2083543; https://doi.org/10.1117/12.2083543


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