## 2 Materials and Methods
### The Design of the Combined Metrics Based on Neural Networks  
One of the main results obtained in earlier papers [11; 24; 70] concerning the use of neural networks is the confirmation of their high efficiency for the optimization of full-reference combined metrics. As the result of multiple parameters optimization, combined metrics based on neural networks provide several benefits. For a given image database they usually outperform any single elementary metric, and it is enough to use a simple NN model with several layers to achieve that result. Therefore, this stage is characterized by high computational performance, and the duration of computations is determined primarily by the slowest metric (in the case of parallel computations). In this paper, an approach tested previously on full-reference metrics has been applied to no-reference metrics and verified experimentally for the NA subset and the whole TID2013 database. Some preliminary results may also be found in [24], although only general-purpose metrics have been designed, demonstrating quite limited universality, given the results obtained for different considered datasets. Since the use of more complex deep learning models [71; 72] may not always be applicable for different image processing tasks, due to its limitations on the structure and size of the trained model and its computational complexity, the experiments are focused on the application of simpler NN models. Taking into account the distortions characteristic for RS images, some additional NR metrics, not considered previously in [24], have been included in calculations, increasing the possibilities of their choice and optimization. Since the accuracy values of even the best NR metric (IL-NIQE) are quite low, a remarkable improvement may be expected using the combined NN metric, potentially better than using both approaches considered above (weighted product and weighted sum). Nevertheless, it would be difficult to directly compare the obtained combined metric with the results presented in [24], since the target datasets for the NN differ significantly. However, based on the results for 11 metrics and the fact that the NA subset has been included as a part of previous experiments, the expected improvement should reach the SROCC values at least 0.75-0.8 for a comparable number of metrics. When designing and training a neural network, it is necessary to take into account some conditions that significantly affect its efficiency:  
Input and output data of the neural network. * The values of the visual quality metrics are used as inputs. The NN result should be an indicator corresponding to the human visual system (HVS). Therefore, the target data are the MOS estimates of the test image databases and the accuracy of the  
Figure 1: Illustration of the relative processing time of elementary metrics listed in Table 1 with respect to the fastest one (WNJE) presented in the logarithmic scale. approximation of the NN result to the MOS estimates determines its effectiveness. For the training and validation phases, the datasets are randomly subdivided into 70% and 30% subsets, respectively;
* The number of the applied metrics. * One of the design goals is to keep computational complexity possibly low, so a smaller number of metrics is preferable. To analyze the influence of the number of input metrics on the overall efficiency, neural networks with different numbers up to over 40 metrics are considered;
* The choice of the applied metrics. * Based on the research results for the reference metrics of visual quality in [11], the regression analysis approach using the Lasso method is quite effective. This method allows us to reduce the complexity of the network by assigning zero weights for non-essential features (elementary metrics in our case). By using different thresholds, we can define the \"cut-off\" levels for each of the possible metrics, thereby determining their importance in the resulting composite metric.