# Data-Driven Calibration Estimation for Robust Remote Pulse-Oximetry
## 3 Results  
We computed the results for both the model-based calibration model of Section 2.2.1 and the calibration determined by the proposed data-driven, empirical approach. To estimate the APBV signature vector sets for the two and three wavelength combinations, we used 5-fold cross validation, resulting in the calibration models:  
Two wavelengths  
\[\vec{P}_{bv}^{s}=\begin{bmatrix}0.323/0.561\\ 1\end{bmatrix}_{[\lambda_{1},\lambda_{2}]=[675760,905]imn},\vec{P}_{bv}^{u}= \begin{bmatrix}0.0195/0.0119\\ 0\end{bmatrix}_{[\lambda_{1},\lambda_{2}]=[675760,905]imn}, \tag{9}\]  
Three wavelengths  
\[\vec{P}_{bv}^{s}=\begin{bmatrix}0.417/0.725\\ 1\\ 1.296/1.294\end{bmatrix}_{[\lambda_{1},\lambda_{2},\lambda_{3}]=[675760,800,905] imn},\vec{P}_{bv}^{u}=\begin{bmatrix}0.0226/0.0119\\ 0\\ -0.0054/-0.0052\end{bmatrix}_{[\lambda_{1},\lambda_{2},\lambda_{3}]=[675760,800,905]imn}. \tag{10}\]  
The APBV vector for all four wavelengths was derived from the two 3-wavelength models of Equation (10), where the values for the 905 nm wavelength were calculated as the mean of the [675,800,905] nm and [760,800,905] nm calibration models.  
We computed the SpO\({}_{2}\) values with processing windows of 10 s, a step size of 1 s and used a 10 s moving average filter as post-processing. To prevent clipping which biases the results, we sampled pulse signature vectors within the SpO\({}_{2}\) range 75-110%, with a sampling resolution of 0.1%. The overall results are displayed in Table 1. The average SpO\({}_{2}\) traces of the dataset (\(n=25\)) calculated with two three-wavelength combinations for both the model-based and the empirical calibration model are visualized in Figure 8. A visualization of the SpO\({}_{2}\) traces for all recordings is displayed in Figure 9. It can be observed that, although the same breathing protocol was used for all recordings, the dynamics are not identical. An overview of the evaluation metrics (pulse) quality, RMSE and bias for all recordings in the dataset using the model-based and empirically-derived calibration models is provided by Figure 10.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline \multirow{2}{*}{**Evaluated Wavelengths**} & \multicolumn{2}{c}{**RMSE (\%)**} & \multicolumn{2}{c}{**Bias (\%)**} \\ \cline{2-5}  & **Model** & **Empirical** & **Model** & **Empirical** \\ \hline
[675,905] nm & 2.16 & 1.33 & \(-\)1.77 & 0.06 \\
[760,905] nm & 4.64 & 1.63 & 4.34 & 0.06 \\ \hline
[675,800,905] nm & 1.87 & 1.11 & \(-\)1.53 & \(-\)0.03 \\
[760,800,905] nm & 5.46 & 1.39 & 5.22 & 0.01 \\ \hline
[675,760,800,905] nm & 2.48 & 1.93 & \(-\)0.47 & 0.11 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The overall results for the model-based and empirical, data-driven APBV calibration model.  
Figure 8: The average SpO\({}_{2}\) traces for the dataset (\(n=25\)) using the two evaluated three-wavelengths combinations, where the \(\Delta\)SpO\({}_{2}\) induced by the breathing protocol can be clearly observed.  
Figure 9: An overview of the SpO\({}_{2}\) traces from all the recordings in the dataset (\(n=25\)) shows the necessity of the proposed empirical calibration approach.