RANDOM NOISE ASSESSMENT IN AERIAL AND SATELLITE IMAGES

Random noise in aerial and satellite images is one of the factors, decreasing their quality. The noise level assessment in images is paid not enough attention. The method of numerical estimation of random image noise is considered. The object of the study is the image noise estimating method, based on harmonic analysis. The capability of using this method for aerial and satellite image quality assessment is considered. The results of the algorithm testing on model data and on real satellite images with different terrain surfaces are carried out. The accuracy estimating results for calculating the root-mean-square deviation (RMS) of random image noise by the harmonic analysis method are shown.


INTRODUCTION
Image's quality in terms of it's visual perception is one of the most important characteristics. It directly affects the quality and volume of information transmitted by images about terrain objects. There are many factors that affect the aerial and satellite image's quality, which are determined both by surveying conditions (cloud cover, haze, illumination, etc.) and by technical means of obtaining and processing images. Among factors, reducing the image's quality is digital noise, which appear in image as randomly located pixels with significantly different brightness or color from average brightness or color of neighboring pixels (Khryashchev, 2011;Lapshenkov, 2012). Random noise affects the interpretation quality of aerial and satellite images, that's why its level must be determined when performing production works to assess the suitability of this data for creating the final geospatial products based by them. This task also arises when performing testing and validation of remote sensing satellite systems that are being put into operation. The most noticeable effect of random noise on interpretation image quality becomes when detecting low-contrast objects and objects that fall into the shadow of high-rise structures, an example is shown in Figure 1. The causes of random image noise are both camera specifications, such as physical pixel size, matrix sensitivity, temperature, etc., and surveying settings, as the value of the exposure (Zotov, 2015). There is a number of publications devoted to determining the aerial and satellite image noise level topic (Beloglazov et al., 2009;Schowengerdt, 2010, Yi et al., 2018, Lim et al., 2018, but in general, this problem is not given enough attention, and in practice, the noise level indicator is not always being assessed when evaluating the images quality, despite its obvious influence on interpretation properties. Sufficient number of researches are devoted to random noise removing to improve the images quality (Donoho, 1995;Lin, S. and Xiaosu, G., 2020), but this is not the purpose of this study, due that these algorithms unavoidably affect the geometric properties of an image. The performance of aerial and satellite surveys is associated with assessing the quality of obtained materials, that carried out at images primary post-processing stage. Currently, the images quality assessment is executed visually by the operator. This method allows only a qualitative image's assessment by its brightness and contrast characteristics, and color balance, taking into account the peculiarities of the operator's psychophysical perception. The subjectivity of such assessment is beyond doubt. In this way it is not possible to estimate the noise level, which is often visually noticeable in the image. The statement about the random image noise presence without determining its quantitative assessment only based on visual analysis has a few worth. Figure 2.a shows a piece of an image scene, obtained by Canopus-B spacecraft, and an image, obtained by airborne camera DMC II in Figure 2.b. Both images show a visually noticeable random noise. There are various ways to assess the image noise and there are a lot of research work devoted to this issue, which describe the algorithms and perform their comparative analysis (Samoilin, 2006;Chen et al, 2019;Lapshenkov, 2012;and others) There is a number of publications devoted to determining the aerial and satellite image noise level topic (Beloglazov et al, 2009;Schowengerdt, 2010), but in general, this problem is not given enough attention, and in practice, the noise level indicator is not evaluated at all when assessing the images quality, despite its obvious influence on interpretation properties. Lapshenkov (2012Lapshenkov ( , 2013 proposed an algorithm for assessing the image noise level based on harmonic analysis. The author shows the advantage of the proposed algorithm in comparison with alternative methods, and presents the experimental results, in which the algorithm based on harmonic analysis allows to obtain the most accurate assessing of the random image noise level.
The purpose of the study is to test the reliability of the image noise estimation algorithm based on harmonic analysis and the possibility of its application for assessing the aerial and satellite images quality, obtained for mapping purposes.

METHODOLOGY
To test the proposed noise estimation algorithm and the possibility of its application for assessing the aerial and satellite images there are several tasks to be solved: to estimate the accuracy of the algorithm on the model data; to estimate the algorithm's resistance to the type (contour load) of the underlying surface; to analyse the obtained results and evaluate the algorithm's accuracy.
The signal-to-noise ratio is used as a measure of the noise impact on image's quality. It is known different ways to evaluate this indicator. Shovengerdt (2010) gives the following methods: the signal-to-noise contrast ratio (1) as an «amplitude» estimate or the squared contrast ratio can be used to estimate the noise «power» (2): where: Csignal = contrast value of signal C noise = contrast value of noise.
The noise influence on image's quality also can be assessed as the standard deviations (RMS) ratio of signal and noise levels: or as a variance ratio: where: σsignal (S) = RMS of pixel values for the image signal σ noise (NRMS) = RMS of pixel values for the image noise.
Often, the logarithm of the signal-to-noise ratio is used as a random noise level indicator in decibels (Lapshenkov, 2012;Schowengerdt, 2010): The image noise estimation method, proposed by Lapshenkov, allows to determine the random noise RMS (NRMS) based on harmonic analysis, so it is expedient to use the formula (3) to calculate the signal-to-noise ratio.
In Lapshenkov (2012Lapshenkov ( , 2013) the implementation of methods for estimating the image noise, including those based on harmonic analysis, in the MATLAB is presented. The proposed method is based on the analysis of spectral power density distribution of the signal, describing the image. This distribution is calculated using the two-dimensional Fourier transform. In this article, the implementation of proposed method for estimation image random noise is performed in Python 3.x. The program code of the respective function is shown below. The signal RMS can be calculated by (6), under the assumption that it is uncorrelated with noise: where: σtotal = RMS of total pixel values calculated from the image.

Estimation the accuracy of the algorithm on the model data
A sample of test images for the initial verification of the random noise estimation algorithm, based on harmonic analysis, was created. Images were obtained by adding random gaussian noise with different RMS: NRMS = 1, 2, 3, 4, 5, 10, 20, 40, 80 to the artificially created gray wedge's original image with a noise RMS NRMS = 0. The artificial noisy images sample is shown in Figure 3.   Table 1 shows that the harmonic analysis method can provide the image noise RMS assessing with an average absolute error about 7,7%. Figure 3 shows the graphs of the reference random image noise RMS (NRMS) for the test sample and random noise RMS, calculated by the harmonic analysis method (NʹRMS). Assuming the graphs in Figure 4 and calculations in Table 1, it is obvious that with an increase in the image's noise RMS, the error of its determination also increases.

Estimation the algorithm's resistance to the underlying surface type (contour load)
To estimate the stability of the random noise assessing method, based on harmonic analysis, to the type (contour load) of the underlying surface, a test sample of satellite images with various terrain types was created. There are five main terrain types: a. urban areas (multistorey buildings), b. industrial facilities, c. village settlements, d. agricultural lands, e. relief features.
The images were obtained by Canopus-V spacecraft No. 6. Sample images are shown in Figure 5. Based on each of these images, a sample, similar to the test sample described above, was created by adding the random gaussian noise with above RMS values. There were 5 samples in total. The noise RMS was estimated taking into account the native image noise of the original image noise NRMS base. The results of random noise assessing based on harmonic analysis for satellite image samples and their accuracy assessment are shown in Table 2 The results in Table 2 indicate that harmonic analysis method showed a stable result when assessing images with different types of terrain surface. It confirms the method's invariance to this factor and the possibility of it's application for assessing the quality of aerial and satellite images.

The analysis of the obtained results and evaluation the algorithm's accuracy
Evaluation of the algorithm's accuracy was in calculating the error (in percentage) with which the random image noise RMS can be determined. The accuracy evaluation results are shown in Table 3. The obtained in Table 3 results show that the reviewed method allows to assess the random image noise RMS with an average absolute accuracy about 12,7%. For random noise assessing in this study the panchromatic images were used. When estimating the noise level of color images, the calculation should be performed in grayscale mode or separately for each color channel, when the detailed analysis is required.

CONCLUSION
In aerial and satellite image quality assessing the random image noise should be evaluated as one of the important quality characteristic in terms of visual perception. In this study the possibility of the image noise estimation algorithm, based on harmonic analysis, for assessing the aerial and satellite images was tested. The method's test consisted in the estimation of it's accuracy on the model data. A sample of artificial images with random noise RMS of values from 0 to 80 was used. The algorithm showed the results of a high accuracy. The next step of the study was the algorithm's resistance estimation to the type (contour load) of the underlying surface. Five samples of satellite images with different terrain types were formed for this with random noise addition. The added images noise RMS were the same values, as they were on a previous step for the model data. The obtained results confirmed the stability of a harmonic analysis method to different types of terrain surface and the possibility of it's application for aerial and satellite image quality assessment. The final step of the study showed, that the harmonic analysis method allows to assess the random image noise RMS with an average absolute accuracy not worse than 13 %.