Application of high frequency filtration to remove cloudiness in Earth remote sensing images

. At present, methods of digital processing of Earth remote sensing images are widely used to improve the image quality. For example, many images are discarded due to high clouds in the images, which obscure objects of interest. In this paper, the possibility of using high-frequency global filters to reduce cloudiness in the image is considered, and the results of image enhancement are shown.


Introduction
At present, methods of digital processing of Earth remote sensing (ERS) images are widely used to improve the image quality. But many original images contain distortions, for example, high clouds, which partially or completely hide objects of interest. The possibility of preliminary ranking or selection of images with respect to the prevalence and location of clouds in the image should significantly reduce the search time for suitable images for solving applied problems [1].
Another common way to improve such images is preliminary processing of remote sensing data: radiometric, atmospheric or geometric correction [2]. It is also possible to use classical methods of spatial filtering of digital image processing [3]. In this paper, we will consider the possibility of applying global high-frequency filtering methods to eliminate cloudiness of remote sensing images.

Method description
Consider, as the initial data, a snapshot of remote sensing of the Earth of the vicinity of the Taseevsky district of the Krasnoyarsk Territory ( Figure 1). As a distortion of the cloudiness of the image, the smoke in this area is presented, and the central part of the image contains a high degree of distortion, and the lateral left one is already less [4]. For the convenience of calculations, let us set the size of the investigated area as a power of two: 512 * 512 pixels (the use of the Fourier transform of two-dimensional signals with a number of samples other than a power of two is described in [5][6]). This image can be represented as a function f(x,y) of the brightness of a pixel with coordinates x and y, taking integer values 0-255 for each red, green, blue channel in the RGB color model.
In [3], it is proposed to multiply all the image elements f(x,y) by , and then calculate the discrete Fourier transform of this function. In this case, we get a centered Fourier transform F(u,v) in the frequency domain, in which high frequencies (responsible for image contours and sharp transitions) will be in the center of the spectrum, and low frequencies (responsible for image smoothing and color saturation) will be around the edges.
We apply a global high-pass filter to the obtained function F(u,v), for example, a Gaussian high-pass filter (HPF): where is the distance from the center of the Fourier transform to the point with coordinates , is the cutoff frequency. The Gaussian HPF graph is shown in Figure  2. Fig. 2. Graph of a Gaussian LPF function on the left, a grayscale image of the filter in the center, radial filter profiles for different values of D 0 on the right As a result of filtering, the high frequencies will remain unchanged, and the low frequencies outside the radius D 0 will be zeroed. After that, we calculate the twodimensional inverse Fourier transform, multiply all samples of the resulting function by to cancel centering, and get the processed image f 1 (x,y).

Obtained results
The result of filtering is shown in Figure 3. The image has sharp outlines of objects, there is no color saturation. At the same time, the rather rare smoke on the left side of the image is no longer visible, but a denser, outlined haze in the center remains noticeable.

Conclusion
On the example of a photo of a smoky surface of the Taseevsky district of the Krasnoyarsk Territory, a method of applying global high-frequency filtering to improve the image is shown. As a result of processing, the sparse haze on the left side of the original image becomes less noticeable. At the same time, dense smoke in the center became more rarefied, but did not disappear completely, since in the high-frequency spectrum the boundaries of this cloudiness have a significant effect on the image.