A Moreau Envelope-Based Nonlinear Filtering Approach to Denoising Physiological Signals

The recovery of an unknown (or minimally known) physiological signal embedded in noise has been an indispensable topic drawing the attention of many researchers. Restoration of these signals through conventional linear filtering schemes induces oversmoothing effect at jump discontinuities, and most of the nonlinear filters do not perform well at large noise level. In this paper, we propose a new nonlinear filtering approach, which incorporates the majorized version of a class of nonsmooth functions integrated with Moreau envelope-based regularization. By relaxing the strict sparsifying penalty, the new algorithms balance the smoothness property and the piecewise characteristics of biosignals. We provide the optimality criterion for the proposed algorithms. These algorithms recover the source signals from their noisy measurements. The algorithms outperform the state-of-the-art methods for piecewise synthetic and real-world physiological signals corrupted by additive noise.