Signal segmentation and denoising algorithm based on energy optimisation

A nonlinear functional is considered in this short communication for time interval segmentation and noise reduction of signals. An efficient algorithm that exploits the signal geometrical properties is proposed to optimise the nonlinear functional for signal smoothing. Discontinuities separating consecutive time intervals of the original signal are initially detected by measuring the curvature and arc length of the smoothed signal. The nonlinear functional is then optimised for each time interval to achieve noise reduction of the original noisy signal. This algorithm exhibits robustness for signals characterised by very low signal to noise ratios.