Generalized Inverse Hyperbolic Sine Regularization to Detect Transient Signal and to Reduce Noise in Biomedical Time Series

Various biomedical signals, such as the near-infrared spectroscopy (NIRS) time series, are essential in many health science technologies. A major challenge in processing these signals is artifact contamination. The specific information of the NIRS time series motivates separating this series into the low-frequency and high-frequency (transient and sparse) signals. Therefore, we present a novel algorithm to detect the transient signal and to reduce noise in this series and related signals. Numerous studies have shown that the penalized least squares regression (PLSR) based on the non-convex regularization is a well-known method to address our problem. Hence, we present the non-convex generalized inverse hyperbolic sine regularization and its multivariate shrinkage function (proximal operator) derived via PLSR for our proposed method. The synthetic and realworld (NIRS) signals are used to compare the performance of the competing methods and the proposed method. Experimental results demonstrate that our method can detect the transient signal and reduce noise more effectively than the state-of-the-art methods.