An Exploratory Method for Smooth/Transient Decomposition

Abstract: We consider a separation problem where the observation consists of the sum of a high amplitude smooth signal and a low amplitude transient signal. We propose a method for decomposition that relies on solving instances of a `constrained filtering problem', which is posed as a convex minimization problem. We provide a fast algorithm for solving the minimization problem, and demonstrate the effectiveness of the scheme for a vital signs monitoring experiment using radar.