Arterial pulse estimation using autoencoder

Based on the explained sensing model, each pulse signal from the sensor output X_i at the skin is related to the source signal of the pulsatile activity Y at the artery deep inside the tissue through the discussed transfer function of a filter h that is defined by certain weights b_n and depends on the sensing location. Our objective is to reconstruct the hidden arterial pulse signal Y from the measured pulse signals from multiple sensors outputs X_i at different sensing locations for i = 1 to K where K is the number of sensors.

We propose using the unsupervised machine learning algorithm of autoencoder to estimate the arterial pulse signal Y from the input pulse signals X_i. The autoencoder is capable of estimating a lower dimension representation, called the code, from the higher dimension inputs. The autoencoder consists of an encoder network that encodes the inputs from the input layer into a lower dimension representation in the hidden layer which is decoded by the encoder network to reconstruct the inputs at the output layer as shown in Figure ^S6. The layers of the encoder and decoder networks are implemented as neural networks and their weights are estimated through the gradient descent optimization method to minimize the error between the input and output layers by minimizing the loss function which is the square error between the input and output layers. As the number of sensors K and the dimension of the input increases, the accuracy of the code estimation increases.

The autoencoder can accurately estimate the arterial pulse signal when the decoder network is equivalent to the transfer functions h that maps the Y at hidden layer to the measured pulse signals X_i and in this case, the encoder network represents the target reconstruction function that reconstructs the arterial pulse from the input observations. This goal is achieved by implementing the encoder and decoder networks as convolutional neural network (CNN) with a linear activation layer which consists of a window of weights that sweeps the input dimensions similar to the operation of the filter that model the pulse transfer function. The input pulse signals are divided into overlapping time segments which are considered the input samples for the training of the CNN networks of the autoencoder. After the gradient descent optimization and minimizing the loss function, the weights of the encoder CNN are used to estimate the arterial pulse signal from the input signals which is used to extract the BP features for BP estimation using the regression models.