Signal denoising based on the Schrödinger operator's eigenspectrum and a curvature constraint

Abstract The authors propose an adaptive, general and data‐driven curvature penalty for signal denoising via the Schrödinge operator. The term is derived by assuming noise to be generally Gaussian distributed, a widely applied assumption in most 1D signal denoising applications. The proposed penalty term is simple and in closed‐form, and it can be adapted to different types of signals as it depends on data‐driven estimation of the smoothness term. Combined with semi‐classical signal analysis, we refer this method as C‐SCSA in the context. Comparison with existing methods is done on pulse shaped signals. It exhibits higher signal‐to‐noise ratio and also preserves peaks without much distortion, especially when noise levels are high. ECG signal is also considered, in scenarios with real and non‐stationary noise. Experiments validate that the proposed denoising method does indeed remove noise accurately and consistently from pulse shaped signals compared to some of the state‐of‐the‐art methods