## 1 Introduction  
The heart rate (HR) is one of the most important cardiac signals in the human body. The HR can be used to monitor medical emergencies and to determine general medical health. However, when measuring the HR, it is often difficult to apply measurement sensors in daily life outside of specific situations because of the restriction of human activity caused by attached sensor. Also, patients who have skin irritations in medical institutions such as hospitals can experience difficulty due to direct contact of the sensor with the skin. Overall, people experience a great deal of discomfort if any sensor is attached to their body parts. Non-contact HR measurement can overcome these problems. This approach is based on the fact that HR signals can be detected via the human skin [1], with optical changes on the skin surface visible due to blood perfusion caused by the heartbeat. The optical variation caused by heartbeats is very subtle, meaning that the accurate detection of cardiac signals was studied in great detail. For example, in Reference [2], the green channel produced the strongest photoplethysmography (PPG) signal among the red/green/blue (RGB) image channels; thus, it was analyzed in the frequency domain as an HR feature [3]. In addition, [PERSON] et al. delicately cropped the face region and then applied an adaptive filter to determine the difference between the face and the background regions based on the assumption that there is a motion correlation between the two regions [4]. However, although the green channel can reflect PPG variation, using this channel only can generate severe noise. To overcome this, blind source separation (BSS) was proposed. [PERSON] et al. reported an HR estimation method using independent component analysis (ICA) with a webcam [5; 6]. The webcam took RGB image sequences of the subject's face, and the RGB images were separated into three motion reflecting source components. Each source component was then analyzed by comparing it with the HR ground-truth, and the second component was selected, showing the best similarity fit with the ground-truth, as the desired HR source component. In Reference [7], joint blind source separation (advanced BSS), with the goal of source separation while maintaining consistent sources across multiple datasets, was applied to denoise facial signals. [PERSON] et al. attempted to detect HR signals by magnifying subtle source components based on changes to skin color due to the pulse [8]. However, applying this in real-world situations is limited because most signals are significantly larger than the color variation caused by the HR, meaning that it can only operate under controlled conditions, e.g., with no motion or changes in illumination. An approach that linearly combines observation signals was introduced by [PERSON] et al. [9]. It was based on the use of RGB channels under the assumption of a standardized skin tone, and several linear combination features extracted from the RGB signals were compared under equal conditions. [PERSON] et al. then proposed a spatial pruning and temporal filtering method that improved upon previous linear combination features [10]. After the pruning procedure, the HR was extracted using principal component analysis (PCA) based on the assumption that a periodic signal such as the HR should have the highest variance because subject motion is occasional. Deep-learning-based approaches were also proposed. [PERSON] et al. built a feature map learning framework using synthetic spatiotemporal maps to overcome the problem of limited training data [11]. The estimator model pre-trained using ImageNet was trained on the synthetic data and fine-tuned using limited real facial data. Relying on the same deep-learning method, [PERSON] et al. used a convolutional neural network (CNN) for region-of-interest (RoI) selection divided into three stages: face detection, tracking, and skin-region selection [12].