Transient Artifacts Suppression in Time Series via Convex Analysis

This book chapter addresses the suppression of transient artifacts in time series data. We categorize the transient artifacts into two general types: spikes and brief waves with zero baseline, and step discontinuities. We propose a sparse-assisted optimization problem for the estimation of signals comprising a low-pass signal, a sparse piecewise constant signal, a piecewise constant signal, and additive white Gaussian noise. For better estimation of the artifacts, in turns better suppression performance, we propose a non-convex generalized conjoint penalty that can be designed to preserve the convexity of the total cost function to be minimized, thereby realizing the benefits of a convex optimization framework (reliable, robust algorithms, etc.). Compared to the conventional use of ℓ 1 norm penalty, the proposed non-convex penalty does not underestimate the true amplitude of signal values. We derive a fast proximal algorithm to implement the method. The proposed method is demonstrated on the suppression of artifacts in near-infrared spectroscopic (NIRS) measures.