The Suppression of Transient Artifacts in Time Series via Convex Analysis

For the suppression of transient artifacts in time series data, we propose a non-convex generalized fused lasso penalty for the estimation of signals comprising a low-pass signal, a sparse piecewise constant signal, and additive white Gaussian noise. The proposed non-convex penalty is designed so as 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 L1 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.