Improvement of images by using graduate transformations of their Fourier depictions

Abstract

The object of research is low-quality digital images. The presented work is devoted to the problem of digital processing of low quality images, which is one of the most important tasks of data science in the field of extracting useful information from a large data set. It is proposed to carry out the process of image enhancement by means of tonal processing of their Fourier images. The basis for this approach is the fact that Fourier images are described by brightness values in a wide range of values, which can be significantly reduced by gradation transformations. The work carried out the Fourier transform of the image with the separation of the amplitude and phase. The important role of the phase in the process of forming the image obtained after the implementation of the inverse Fourier transform is shown. Although the information about the signal amplitude is lost during the phase analysis, nevertheless all the main details correspond accurately to the initial image. This suggests that when modifying the Fourier spectra of images, it is necessary to take into account the effect on both the amplitude and the phase of the object under study. The effectiveness of the proposed method is demonstrated by the example of space images of the Earth's surface. It is shown that after the gradation logarithmic Fourier transform of the image and the inverse Fourier transform, an image is obtained that is more contrasting than the original one, will certainly facilitate the work with it in the process of visual analysis. To explain the results obtained, the schedule of the obtained gradation transformation into the Mercator series was carried out. It is shown that the resulting image consists of two parts. The first of them corresponds to the reproduction of the original image obtained by the inverse Fourier transform, and the second performs smoothing of its brightness, similar to the action of the combined method of spatial image enhancement. When using the proposed method, preprocessing is also necessary, which, as a rule, includes operations necessary for centering the Fourier image, as well as converting the original data into floating point format.