## 4 Discussion  
The visual analysis of scatter plots presented in Figure 2c,d shows one important benefit of the NN-based combined metrics. The dependence of the metric on MOS values is practically linear and this produces high SROCC and PLCC, simultaneously. This is caused by the fact that MOS values have been used as the target function in the NN training. For the designed \(CM_{5}^{+}\) metric based on the weighted sum (Figure 2b) the dependence is not linear and, due to this, PLCC can be sufficiently smaller than SROCC. Meanwhile, this drawback can be easily removed by an appropriate fitting made after the calculation of \(CM^{+}\) and optimization of its coefficients. For some of the \(CM\) and \(CM^{+}\) metrics, particularly based on the combination of a relatively small number of elementary metrics, the optimization of their coefficients according to the maximization of Spearman's correlation, has led to very low values of Pearson's correlation and high nonlinearity of the relation between them and MOS values. One of the possible approaches to avoid this problem is the choice of the PLCC as the goal function, similarly as in some earlier papers [29, 30], however, in this case, smaller SROCC values may be achieved. Although for 5 elementary metrics better SROCC results may be obtained using the weighted sum, even in comparison with the NN-based approach, the advantages of the neural networks may be observed when more elementary metrics are used as inputs, as illustrated in Figure 3.  
The choice of elementary metrics made by the Lasso algorithm during the NN-based design differs from the \"best\" combinations used in the \(CM\) and \(CM^{+}\) metrics. Comparing the case of five elementary metrics, the following metrics have been selected by the Lasso: SISBLIM_WFB, IL-NIQE, HOSA, CORNIA, and MSGF, whereas the highest SROCC value for the \(CM_{5}^{+}\) metric has been obtained for the combination of ARISMC, IL-NIQE, CORNIA, WNJE, and QAC as presented in Table 5. Interestingly, only two of the metrics selected in these two cases are the same. As shown in Table 8, for 10 elementary metrics, the performance of the NN-based metric is the best for 4 out of 5 subsets of the KADID-10k database and close to the best in the remaining case. Thus, in general, although optimized for the database TID2013, the performance of the designed NN-based metrics is appropriately good for other databases. The results presented in the paper confirm the usefulness of the various combination methods of elementary no-reference image quality metrics for the evaluation of images subject to distortions typical for RS images. Nevertheless, considering the results obtained for the whole TID2013 database, further experiments would be necessary to improve the correlation of such metrics with subjective quality scores as well as for the enhancement of the universality of the combined NR metrics. A design of such metrics sensitive to various types of distortions should be one of the natural directions of further research. Figure 4: Scatter plots obtained for five elementary metrics and the NN-based combined metric for the KADID-10k database: (**a**) HOSA; (**b**) IL-NIQE; (**c**) SISBLIM_WFB; (**d**) MSGF; (**e**) CORNIA; (**f**) combined NN-based metric using 5 inputs. **Author Contributions:** Conceptualization, A.R., O.I., V.L. and K.O. ; methodology, A.R., O.I., V.L. and K.O. ; software, A.R., O.I. and K.O. ; validation, O.I., J.F. and K.O. ; formal analysis, O.I. and V.L. ; investigation, A.R., O.I, V.L. and K.O. ; resources, A.R., O.I. and K.O. ; data curation, A.R., O.I. and K.O. ; writing--original draft preparation, O.I, V.L. and K.O. ; writing--review and editing, V.L. and K.O. ; visualization, O.I., J.F. and K.O. ; supervision, V.L. and K.O. ; project administration, V.L. and K.O. ; funding acquisition, V.L. and K.O. All authors have read and agreed to the published version of the manuscript.