An Antinoise-Folding Algorithm for the Recovery of Biomedical Signals From Noisy Measurements

Abstract

Sparse sampling (SS) has shown a significant promise for the recovery of biomedical signals from noisy measurements. In practice, the premeasurement noise, i.e., the noise associated with the unprocessed signal is often ignored. At large compression, a small perturbation in the raw signal may degrade the signal-to-noise ratio by a significant amount due to the noise-folding effect. In this paper, a new antinoise-folding sparse recovery framework is proposed, which is blind-to-noise-statistics, and it does not require any prior warm-up step to select the starting point. The source signal is recovered from the noisy measurements by solving a nonconvex regularization-based constrained minimization problem followed by a data-adaptive Stein’s unbiased risk estimate-based denoising process. The constrained problem is linearized by employing the method of majorization–minorization. Furthermore, the sparse recovery analysis of the new algorithm is established. The numerical test results obtained by employing noisy photoplethysmogram data and real-world fetal-electrocardiogram data show the superior performance of the proposed method as compared with various state-of-the-art SS methods.