## 1 Introduction
In [23], multiple statistics features sensitive to image quality have been extracted from hyperspectral images and used for the IQA. A particular application of hyperspectral data restoration and super-resolution has been studied. One way of improvement of metrics performance has been found expedient recently- to design and optimize the so-called combined metrics [11; 24; 29; 30]. The term \"combined\" means that several \"elementary\" (quite simple) metrics are calculated sequentially or in parallel, and then united (combined) in a certain manner. In this way, particular drawbacks and weaknesses of elementary metrics can be eliminated while their positive features can be sufficiently enforced with a synergetic effect. Combining or aggregation can be performed in different ways: using \"robust\" processing with the preliminary fitting of metric to MOS dependencies [24], by simple calculation of a weighted sum or product of elementary metrics [29; 30], or employing a trained NN. Although some promising results have been obtained in [24], the analysis for particular types of distortions typical for RS images has not been presented. The appropriateness of such an approach has also been confirmed for video quality assessment by the successful development of the Video Multi-method Assessment Fusion (VMAF) metric by Netflix, validated by RealNetworks [31]. In all cases, one needs certain databases or their parts to carry out training or to employ optimization of the combined metrics as well as to verify the results. Unfortunately, there are no special commonly accepted databases for RS images with MOS determined for them. There are several reasons behind this. First, there are RS images of different nature (optical, infrared, and radar) and characteristics (noise type and intensity, number of channels, and spatial resolution). Second, while it is possible (although not easy) to attract quite many people to evaluate the quality of standard color images, it is considerably more difficult to find enough qualified experts to assess the quality of RS images. In [11], a slightly \"artificial\" way out has been found since a subset of images from the database TID2013 [27] has been selected, having distortions of type and intensity inherent for three-channel RS images. Using these selected images (subsets Noise and Actual in TID2013), we have trained the NNs that used different numbers of elementary full-reference metrics as NN inputs. As the result, we have obtained the SROCC of about 0.965 for the best structures and configurations of the NN-based metrics for the subset Noise + Actual (NA). Keeping in mind these results, we have decided to carry out a similar attempt and study for NR IQA metrics. Thus, the main novelty of this paper consists in the design of general-purpose combined NR metrics using NN and weighted sum/product-based approaches of elementary metric aggregation with application to distortions typical for three-channel RS images. The paper structure is as follows: in Section 2 the TID2013 database, NR metrics, earlier results, and the applied methodology are discussed, Section 3 focuses on the presentation of experimental results with their analysis. A brief discussion is given in Section 4.