## 1 Introduction  
Significant technological progress in image processing algorithms and ability to improve perception of the world surrounding us using modern deep learning methods has led to invention and enablement of various applications that were previously much harder to implement, e.g., face recognition [1; 2], objects detection and segmentation [3; 4; 5] or image resolution enhancement [6]. Another factor that steers the direction of advances in new applications is the increased capabilities of many electronic digital devices. Medical diagnostics and reasoning systems also benefited from this progress, allowing for real-time vital signs analysis and tracking using standard cameras [7] or wearable devices [8]. The remote measurement of RR has many potential applications in medical diagnostics and screenings like monitoring of newborns or small children in incubators or hospital beds [9], monitoring of the severe acute respiratory syndrome (SARS) [10], support in emotion analysis [11], etc. The use of thermal cameras was proposed to analyze facial images and estimate RR based on a nasal heat flow and described in [9; 12; 13; 14; 15; 16; 17] and other papers. The typical estimation of RR requires a multi step procedure. First, a Region Of Interest (ROI) is detected for each thermal frame representing the source of thermal changes (due to respiration) in the area of nostrils or a mouth. The ROI can be specified manually or can be automatically detected (in a frame or for each frame) and tracked (between frames). In [18], the authors described a particle filter tracker driven by a probabilistic template function that was capable of adapting to abrupt positional and physiological changes. Other authors also proposed ROI tracking methods (e.g., [19; 20]). In the next step, a single value is calculated to represent each ROI. A collection of such values forms a signal representing local temperature changes in time. Finally, a signal is filtered (e.g. removing high frequency components) and a frequency for dominated changes is calculated. It is assumed, that this frequency represents the respiratory rate. In recent years, new portable and cost-effective thermal cameras have been available. For example, FLIR(r) Lepton family cameras [21] are very small (e.g., 10.5 \(\times\) 11.7 \(\times\) 6.4 mm, with an internal shutter) and cost less that 200 USD. These features allow to think about wide application of thermal monitoring, e.g., to support remote diagnosis of elderly people at home (e.g., during a video talk or as a self-diagnostics). However, a spatial resolution of these small thermal cameras is as low as 80 \(\times\) 60 or 160 \(\times\) 120. Small resolution of images could be a problem for detection of facial features or detection of a ROI representing respiration-related temperature changes. Different methods have been proposed in (a visible light spectrum) computer vision to improve low resolution images or to detect (and amplify) small, local changes in videos. Subtle intensity variations introduced in thermal videos of a face due to respiratory activities can be enhanced using Eulerian Video Magnification (EVM [22]) or related algorithms [23; 24]. This technique amplifies intensity differences within a particular frequency spectrum. This works well if the estimate respiratory rate (frequency) is known. Otherwise, noise and motion artefacts are highly amplified. Therefore, some researchers propose to magnify only selected segments within a video [25]. The EVM algorithm has been already successfully used for enhancing vital sign signals [26; 27; 28]. Recently, many different deep-learning algorithms for super resolution have been proposed. It has been proved that such algorithms can efficiently improve the presentation of details in the processed low-resolution (LR) visible light images. One of the first method in this area was SRCNN [29], which implemented a single Convolutional Neural Network (CNN) achieving the state-of-the-art restoration quality.