Real-Time Processing for Weighted Pulse Decomposition of Photoplethysmography Signals Based on Interior Point Method in Wearable Devices for Hemodynamic State

Waveform decomposition technique can be applied to analyze photoplethysmography (PPG) signals from wearable devices for revealing the latent property of hemodynamic state. Solving for the component waves is considered as a constrained nonlinear optimization problem. The interior point method is used with a refined step size during line search. Exact derivatives in Hessian matrix and gradient are adopted in this work to acquire precise results. Inter-dependency and intra-dependency of the derivatives are exploited to reduce 93.7% computation complexity with a storage of only 62 ingredients. The block LDL decomposition with Bunch Kaufman pivoting strategy that takes advantage of symmetry property of Hessian matrix is employed to handle the linear equations described for the step size. Both single-precision and double-precision arithmetic are supported. From the experimental results, failure rate of 1.93% and one-cycle processing time of 0.1s are achieved by our program, which outperforms the commercial solver and the real-time processing requirement can be satisfied to demonstrate its applicability in the wearable devices.