## 2 Materials and Methods  
### Overview of the TID2013 Dataset and Earlier Results in the Combined Metric Design  
To design and verify a new metric, one needs a database or several databases that contain images of a needed type corrupted by distortions with type and intensity inherent for images under interest. Besides, these databases should provide MOS or Differential Mean Opinion Score (DMOS) values for all images. In this sense, there are some problems in the design and verification of visual quality metrics for RS images. First, there is a very limited number of available databases of RS images, and they have a limited number of distortion types and/or are intended for other purposes [32; 33]. Second, remote sensing images of a certain type can be intended for a particular purpose, therefore IQA results can be in improper agreement with this purpose and criteria used. For example, it is currently not fully clear how traditional criteria used in lossy compression relate to criteria characterizing object detection, classification, and segmentation of compressed images. Third, even if RS images have three components, there are several variants of their visualization as RGB color images. If the number of components is larger than three, there are numerous ways to represent RS data in pseudo-colors and then a correspondence between the assessed quality of visualized images and real values of RS data is not clear. Because of this, similarly to [11], the analysis is restricted to three-channel RS images assuming that they are represented as RGB color images. Consideration of more complex cases of more channels (components) of RS images is out of the scope of this paper. Recall that the synthesis and analysis of the full-reference and no-reference quality metrics for RS images using the database TID2013 has already been carried out [11]. The reasons for this may be summarized as follows:  
* The TID2013 dataset contains 25 reference images and images with 24 types and 5 levels of distortions where many distortion types take place in the practice of remote sensing;
* These types of distortions are concentrated in two subsets, namely Noise and Actual, that can be processed and analyzed separately (see the details below);
* MOS values have been obtained for all distorted images in TID2013 including the aforementioned subsets where a larger number of participants (volunteers) have been attracted to experiments (this is important since MOS has to be estimated accurately enough to minimize the negative influence of possible inaccuracy on the SROCC calculation and comparison of metrics performance). The whole TID2013 dataset contains the following types of distortions: Additive Gaussian noise (#1), Additive noise in color components (#2), Spatially correlated noise (#3), Masked noise (#4), High-frequency noise (#5), Impulse noise (#6), Quantization noise (#7), Gaussian blur (#8), Image denoising (#9), JPEG compression (#10), JPEG2000 compression (#11), JPEG transmission errors (#12), JPEG2000 transmission errors (#13), Non-eccentricity pattern noise (#14), Local block-wise distortions of different intensity (#15), Mean shift (intensity shift) (#16), Contrast change (#17), Change of color saturation (#18), Multiplicative Gaussian noise (#19), Comfort noise (#20), Lossy compression of noisy images (#21), Imagecolor quantization with dither (#22), Chromatic aberrations (#23), and Sparse sampling and reconstruction (#24). The distortions ##14, 15, 16, 18, 22, and 23 are atypical for RS applications, other types can be met in multichannel imaging. In this sense, two subsets attract special attention. The subset Noise deals with images having the following types of distortions: Additive Gaussian noise (#1), Additive noise in color components (#2), Spatially correlated noise (#3), Masked noise (#4), High-frequency noise (#5), Impulse noise (#6), Quantization noise (#7), Gaussian blur (#8), Image denoising (#9), Multiplicative Gaussian noise (#19), and Lossy compression of noisy images (#21).