Application of two-dimensional fast Fourier transform algorithm, analog of the Cooley-Tukey algorithm, for 4k fixed format digital image of satellite data in frequency domain processing

Mikhail Noskov,Valeriy Tutatchikov,V.B Kashkin,G.M Tsibulśkii,L.G Sverdlik,V Kharuk,Y.A Maglinets,E Loupian,M.V Noskov

doi:10.1051/e3sconf/202014902010

Mikhail Noskov, Valeriy Tutatchikov + Show 7 more

Open Access

https://doi.org/10.1051/e3sconf/202014902010

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Journal: E3S Web of Conferences	Publication Date: Jan 1, 2020
Citations: 2	License type: CC BY 4.0

Affiliation: Siberian Federal University

Abstract

Currently, digital images in the format Full HD (1920 * 1080 pixels) and 4K (4096 * 3072) are widespread. This article will consider the option of processing a similar image in the frequency domain. As an example, take a snapshot of the earth's surface. The discrete Fourier transform will be computed using a two-dimensional analogue of the Cooley-Tukey algorithm and in a standard way by rows and columns. Let us compare the required number of operations and the results of a numerical experiment. Consider the examples of image filtering.

Highlights

Digital images in the format Full HD (1920 * 1080 pixels) and 4K (4096 * 3072) are widespread
We consider the possibility of using an alternative method - the frequency filtering of such images by calculating the two-dimensional discrete Fourier transform of the function of the brightness of the pixels of the image, applying a filter, and computing the inverse Fourier transform [2]
One way to simplify the calculations is to use the classical algorithm for computing the two-dimensional fast Fourier transform (FFT): first, the one-dimensional FFT using the Cooley-Tukey algorithm for each row consisting of 4096 elements is calculated, and the discrete Fourier transform for each column of 3072 elements

Summary

Introduction

Digital images in the format Full HD (1920 * 1080 pixels) and 4K (4096 * 3072) are widespread. One way to simplify the calculations is to use the classical algorithm for computing the two-dimensional fast Fourier transform (FFT): first, the one-dimensional FFT using the Cooley-Tukey algorithm for each row consisting of 4096 elements is calculated, and the discrete Fourier transform for each column of 3072 elements. In this case, 18*222 + 9*232 = 9234*222 ≈ 9*232 operations of multiplication and 72*222 + 9*232 = 9288*222 ≈ 9*232 addition of complex numbers are required.

Application of a two-dimensional analogue of the CooleyTukey algorithm

Image filtering

Conclusion