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

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.