  This letter presents a novel hybrid method that leverages deep learning to
exploit the multi-resolution analysis capability of the wavelets, in order to
denoise a photoplethysmography (PPG) signal. Under the proposed method, a noisy
PPG sequence of length N is first decomposed into L detailed coefficients using
the fast wavelet transform (FWT). Then, the clean PPG sequence is reconstructed
as follows. A custom feedforward neural network (FFNN) provides the binary
weights for each of the wavelet sub-signals outputted by the inverse-FWT block.
This way, all those sub-signals which correspond to noise or artefacts are
discarded during reconstruction. The FFNN is trained on the Beth Israel
Deaconess Medical Center (BIDMC) dataset under the supervised learning
framework, whereby we compute the mean squared-error (MSE) between the denoised
sequence and the reference clean PPG signal, and compute the gradient of the
MSE for the back-propagation. Numerical results show that the proposed method
effectively denoises the corrupted PPG and video-PPG signal.
