## 2 Background  
There are a number of metrics for blood pressure. Systolic blood pressure (SBP) is the maximum blood pressure and corresponds to the ejection of blood from the left ventricle [2]. After closure of the aortic valve, the arterial pressure decreases, reaching its lowest point at end diastole. This corresponds to the diastolic blood pressure (DBP) [2]. The average blood pressure over the cardiac cycle is known as the mean arterial pressure (MAP). These discrete values are ubiquitous in the clinical setting. However, crucial diagnostic information is also given by the shape of the arterial blood pressure (ABP) waveform. Heart failure, arterial compliance, and valve damage can all be inferred from the waveform's shape [3]. This can assist in patient management. There are two general methods for determining blood pressure: manual auscultation and invasive measurements [1]. In manual auscultation, a cuff is inflated to restrict blood flow. The cuff is then slowly deflated. The sound of the artery through a stethoscope allows the SBP and DBP to be determined [1]. Oscillometric blood pressure measurement works similarly, but is automated [1]. The alternative method is invasive monitoring. A cannula is inserted into an artery (typically the radial or femoral artery), and the blood pressure is measured directly [4]. Cuff-based techniques have the advantage of being non-invasive. However, they cannot be employed for continuous blood pressure monitoring, nor do they provide the ABP waveform. Invasive monitoring allows for both. However, while complications are rare, arterial cannulation does carry risks. These include bleeding, vessel occlusion, and sepsis [4]. Patient discomfort and limitations on patient mobility also restrict where this procedure is applicable. A number of researchers have shown that it is possible to infer blood pressure using photoplethysmography (PPG), which works by shining light on the skin and measuring the intensity of the reflected or transmitted light [5]. The amount of light reflected (or transmitted, depending on the type of sensor) corresponds to blood volume variations [5]. Typically, PPG is employed for pulse oximetry to measure blood oxygen concentration [5]. Two sources of light are shone, and the absorption of each is measured. From this, the concentrations of oxyhaemoglobin and deoxyhaemoglobin can be inferred via the Lambert-Beer Law. The PPG signal is typically used in one of two ways: for model-based methods or learning-based methods. In model-based methods, closed-form equations are derived, from which the blood pressure can be predicted [6]. Learning-based methods instead use supervised machine learning. In the classical approach, the model is trained on features extracted from the PPG signal, as in [7; 8; 9; 10]. The alternative is to train the model on the actual waveform using deep learning (see Refs. [11; 12]). Below we present an overview of some of these works, and a more comprehensive review of the use of machine learning techniques with photoplethysmography for the non-invasive measurement of blood pressure can be found in [13]. The model-based methods are generally based off of the pulse transit time (PTT), the temporal delay between the R-wave and the PPG waveform. [PERSON] et al. [6] made use of the Moens-Korteweg equation, which relates the pulse wave velocity and PTT. By modelling the vessel wall elasticity, they derive an expression for the blood pressure as a function of the PTT and previous blood pressure estimates. Testing on a dataset of 25 patients gave a mean error less than 1 mmHg. The downside of the PTT-based models is the need for a simultaneous ECG measurement and the dependence on physiological constants. Learning-based methods avoid the derivation of models and physiological constants. Instead, the model learns from a dataset. [PERSON] et al. [7] extracted time domain features of the PPG signal, including the crest time (or systolic upstroke duration), diastolic duration, and the pulse widths at different percentages of the pulse height.