# Data-Driven Calibration Estimation for Robust Remote Pulse-Oximetry
## 1 Introduction  
Ensuring adequate oxygen delivery to tissues is a prime objective of acute/critical medical care. Pulse-oximetry allows rapid and convenient measurement of the arterial oxygen saturation with low-cost hardware. It is regarded as the fifth vital sign and enables early detection of hypoxia and screening for critical congenital heart disease (CCHD) [1] and sleep apnea [2]. After the discovery of the basic principle by [PERSON] in the mid-1970s, the first pulse-oximeters were successfully marketed in the 1980s. Nowadays, pulse-oximeters are ubiquitously used in operating theatres, hospital wards, outpatient clinics and general practice surgeries for the monitoring of the critically ill. Before the invention of the pulse-oximeter, invasive arterial blood sampling with subsequent analysis was required. Pulse-oximetry relies on the optical absorption properties of oxygenated and deoxygenated blood measured by a non-invasive optical source-detector geometry, allowing a continuous estimation of blood oxygen saturation. However, pulse-oximeters are prone to motion artifacts and require skin contact.  
Over the last few decades, methods have been presented which allow contactless monitoring of human vital signs with regular cameras in both visible and near-infrared conditions based on the detection of visually imperceptible skin color variations caused by blood volume variations. These vital signs include heart rate and derived features [3], respiration [4; 5], and, more recently, oxygen saturation [4; 6; 7; 8; 9; 10]. Contactless monitoring is especially relevant for: (1) scenarios where direct skin contact should be prevented (e.g., premature infants [11; 12] or patients with extensive burns [13]), (2) spot-check scenarios where a reading should be available within seconds, or (3) scenarios where the current diagnostic procedure could affect the clinical outcome (e.g., with polysomnography for sleep monitoring [14; 15; 16]). The main challenge of contactless measurements is that the signal is generally much weaker compared to its contact-based counterpart and hence more easily distorted. This is particularly detrimental for measurements where amplitudes have to be extracted from individual PPG waveforms, e.g., for the measurement of peripheral blood oxygen saturation (SpO\({}_{2}\)). This motivated the development of an indirect method for the estimation of SpO\({}_{2}\) using SpO\({}_{2}\)-dependent pulse signatures [8], which does not require the individual extraction of amplitudes. This method, denoted \"APBV\" (Adaptive-PBV), showed the feasibility of estimating SpO\({}_{2}\) from distorted PPG signals, e.g., during movement, where the conventional ratio-of-ratios based method renders inaccurate. In order to apply this method, proper calibration is essential. Opto-physiological modelling provides a reasonable estimate but is not sufficiently accurate. Hence, commercially available pulse-oximeters are calibrated based on empirical data.  
In this paper, we present an empirical, data-driven approach to estimate a calibration model for the indirect APBV method which can be applied to an arbitrary number and selection of wavelengths. This is relevant, as in our earlier paper [8], we showed that adding a third wavelength improves the robustness of the measurement. We demonstrate that, based on a dataset with only small variations in SpO\({}_{2}\), an accurate calibration model can be determined which outperforms a calibration model based on modelling of the PPG spectrum. Furthermore, we show that the error only slightly increases using solely near-infrared (NIR) wavelengths when compared to the typical combination of visible red and NIR wavelengths, which confirms our earlier observations [8] and widens the scope for camera-based pulse-oximetry, e.g., for sleep or continuous 24/7 monitoring where patients are monitored in full darkness.