## 2 Materials and Methods
### HR Joint Blind Source Separation  
Unlike the environments tested by previously proposed methods, driving conditions have a lot of dynamic signals. In order to extract the HR from these extreme conditions, sophisticated signal extraction techniques are required. In the present study, before the extraction process, each RGB channel was normalized with a mean unit variance of zero.  
As a noisy component separation technique, our method adopted JBSS. Standard BSS is limited by the necessity to maintain the consistency of the separated source components across different datasets. For example, in ICA, which is a form of BSS, if the source components are separated in the frequency domain, there is a permutation problem in that the separated frequency bins have to be  
Figure 1: Region-of-interest (RoI) selection procedure: (**a**) face detection and cheek region cropping. (**b**) Selected skin region and (**c**) background region except for any skin region where the photoplethysmography (PPG) signal can be detected (the skin region is indicated in yellow).  
aligned. This is caused by blindness to permutation, meaning ICA cannot automatically perform the alignment. Therefore, JBSS is suitable for datasets consisting of several subjects, and it was employed in this paper.  
In the JBSS framework, it is assumed that groups of sources from multiple datasets are uncorrelated, while sources within each dataset are highly correlated. Based on this assumption, independent vector analysis (IVA) was adopted to separate the HR source component from other noise [22]. IVA was devised to solve the permutation problem with Kullback-Leibler divergence between the source and observation joint probability in ICA. The cost function \(C\) was described by  
\[C=K\!I\!\left(p(s_{1},\ldots,s_{L})\parallel\prod_{i}q(s_{i})\right), \tag{1}\]  
where \(p(s_{1},\ldots s_{L})\) and \(\prod\limits_{i}q(s_{i})\) denote the probability density function and the marginal probability distribution function of the source component, respectively. The cost function converged to simultaneously minimize the entropy of all source components, and the mutual information was maximized within each source component. Detrending was then applied to each source component with the smoothing parameter \(\lambda=10\) to remove nonstationary components [23].  
However, as mentioned previously, due to the fact that our algorithm was employed under driving conditions, the use of JBSS only was not sufficient to filter out noisy components. We assumed that there would be residual noise components after the JBSS process. The signals that undergo JBSS can be divided into face and background regions. The HR component should be present in the face region, while other noisy components are present in both regions. This assumption means that there should be some correlation between the face and the background regions. Based on this assumption, the noise components could be excluded, and the HR signal could be retained by subtracting the background signals from the face signals as follows:  
\[HR_{comp}=S_{Face}-S_{Back}, \tag{2}\]  
where \(S_{Face}\) and \(S_{Back}\) are the face and background signals after the JBSS process, respectively. The background region was defined as the uncorrelated region with skin that can emit a PPG signal. The background region is illustrated in Figure 1c. In order to validate this, we plotted the correlation between the face and background results from JBSS for each channel in Figure 2. Because of the presence of significant noise, the correlation coefficients were not strong, but they were positive because a large portion of the noise was present in both the face and background regions.