Denoising by spectral selections of SVD representations of Hankel matricificated data with application to PPG signals

Singular value decomposition (SVD) is a promising tool for denoising corrupted biosignals, e.g., denoising a noisy photoplethysmography recording (PPG). The challenges associated with the SVD method have been tackled in this work, including: 1) selecting the optimal reconstruction components, 2) estimating the optimal rank, 3) estimating the optimal number of data points analyzed based on the target trend/oscillation in the signal. In addition, we propose a denoising method based on SVD to remove both Gaussian white noise (GWN) and baseline wander (BW) from PPG signals. The proposed method is adaptive with respect to the matrix obtained by Hankel matricification of the target signal to 1) eliminate GWN via adaptive dimension reduction by SVD with the aid of a noise level estimator and 2) to remove BW signal using SVD based spectral analysis. The proposed method, which is designated as adaptive SSA-based denoising, gives an excellent denoising performance compared to 4th order Chebyshev II bandpass filter in denoising both simulated/recorded PPG signals.