A Proximity Operator-Based Method for Denoising Biomedical Measurements

Abstract

The reconstruction of biomedical signals from noisy measurements has been an indispensable research topic. A majority of biosignals exhibit typical piecewise characteristics. The recovery of these piecewise biomedical signals embedded in noise through conventional nonlinear filtering schemes fails due to the lack of proper balance between strict sparsity and smoothness-inducing property of regularizers at large noise levels. This work proposes a nonlinear convex optimization-based filtering approach, which incorporates a Moreau envelope-based regularizer using the majorized version of the total variation function. The source signals are restored by exploiting their piecewise characteristics through a majorized cost function. The majorized functions provide some relaxation in solving non-convex functions. The relaxation of the stringent sparsifying penalty provides the balance between the smoothness property and the piecewise features of biosignals. The optimality criterion for the proposed method is analyzed in this work. Furthermore, we evaluate the new method using a standard IoT platform. The recovery performance of this method is found to be superior to various state-of-the-art techniques for piecewise synthetic and real-world physiological signals corrupted by additive noise. © 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.