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

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.