Spatio-Temporal Structure Extraction of Blood Volume Pulse Using Dynamic Mode Decomposition for Heart Rate Estimation

This article proposes a novel blood volume pulse (BVP) signal extraction method for heart rate (HR) estimation that incorporates medical knowledge of the spatio-temporal BVP dynamics. Previous methods merely exploited the spatial similarity of BVPs observed from multiple facial patches and performed the low-rank approximation to extract BVP signals. If noise components are superimposed over the entire face, the previous methods have difficulty distinguishing between the BVP component and noise even in the low-rank subspace. The main novelty of the proposed method is the exploitation of the BVP characteristics in the spatial and temporal domains in a unified manner based on a dynamic mode decomposition (DMD) framework, which is used to extract spatio-temporal structures from multidimensional time-series signals. To analyze the BVP dynamics that exhibit nonlinearity and quasi-periodicity, physics-informed DMD was performed on the time-series signals extracted from facial patches in a time-delay coordinate system. This approach enables the estimation of the DMD modes, which effectively represent the spatio-temporal structures of the BVP dynamics. The other novelty of the proposed method is the incorporation of medical knowledge of the HR frequency band to select the optimal DMD mode. By incorporating this medical knowledge of HR into the proposed framework, the proposed method can accurately estimate the BVP signal and HR. The experimental results obtained using three publicly available datasets yielded a root-mean-square error of the HR estimation results of 6.37 bpm, a 36.5 % improvement over the state-of-the-art methods.