## 4 Discussion  
The evaluation of the proposed CNN-based SR model on both datasets proved that thermal images can be enhanced and lead to improvement of image quality. Both on 8 and 16-bit data enhanced sequences led to higher values of PSNR. In addition, it turned out that on the SC3000 set, the SR model trained on images with even lower resolution (scale 4) outperformed results of the model trained on images down-scaled 2 times. This proves the possibility of improving low-resolution thermal images using deep learning techniques. Although the achieved results are promising, they are only preliminary and we discovered some limitations of the proposed method that should be further investigated. In the best case RMSE of RR estimation was equal 2.46 bpm. In general, the accuracy results are not ideal as in most cases they oscillate around values of 3.5-5 bpm, which is not satisfactory for professional medical applications. Yet, the aim of the study was to evaluate the effect of enhancing very low-resolution images on RR estimation accuracy, which was confirmed as the proposed SR DNN led to a significant decrease of the RMSE. To further reduce the estimation error, we should extend the measurement time and specify more details about data acquisition conditions, e.g., visibility of the nostril area, what has been previously explained in similar studies [44, 46]. Another limitation of the proposed method is the requirement of the manual ROI selection. We believe that the estimation accuracy could be further improved by providing an automatic way of the precise ROI selection. In addition, it could also be interesting to algorithmically detect facial areas where the RR signal is the best to keep human interference to a minimum, as shown in [51]. We would like to include both of these ideas in the future studies conducted in the area of contactless RR estimation. In this study, we analysed short data segments to imitate potential practical applications of the proposed algorithms for home monitoring systems. To increase patients' convenience and avoid influence of body motion on the estimation accuracy, the data acquisition process should be as short as possible. Thus, we experimentally selected lengths of analysed sequences for both datasets. The number of selected samples have a direct effect on frequency resolution and thus on the RR estimation accuracy. For the Lepton dataset 300 samples (\(N\)) were used for RR estimation and the sampling frequency (\(f_{s}\)) was 12 Hz. Thus, the frequency resolution was  
\[\delta f=\frac{f_{s}}{N}*60=\frac{12}{300}*60=2.4\text{ bpm} \tag{3}\]  
Figure 6: The corresponding frame extracted from the Lepton 8-bit sequences used in the study for respiratory rate evaluation. From the left: original, Eulerian Video Magnification, bicubic interpolation scale 2, super resolved using our model scale 2, bicubic interpolation scale 4, super resolved using our model scale 4. Figure 7: The corresponding frame extracted from the SC3000 8-bit sequences used in the study for respiratory rate evaluation. From the left: original, Eulerian Video Magnification, bicubic interpolation scale 2, super resolved using our model scale 2, bicubic interpolation scale 4, super resolved using our model scale 4. For the SC3000 with \(f_{s}=30\) and \(N=400\), \(\delta f=4.5\) bpm. To further improve RR estimation on the SC3000 dataset, more samples could be used. We will investigate this setting in the future study. Other factor influencing the results of RR estimation is selection of the window of samples analysed for RR estimation. This parameter was manually selected by us in the study, yet we believe that the performance can be further improved by automating this process. It's important to note that the problem of RR estimation from thermal sequences in static and dynamic poses have been widely studied in the literature. However, the objective of our study was not to outperform existing RR estimation algorithms, but to evaluate the influence of enhancing thermal data with the SR model on the RR estimation results.