A Comparison of Denoising Techniques with Signals Affected by Non-Gaussian Noise and Sample Entropy as an Indicator of Performance

In this work, we compare three denoising techniques: Wavelet Transform (WT), Multiscale Principal Component Analysis (MSPCA), and Variational Mode Decomposition (VMD). Normally, it is assumed that signals in the process of measurement or transmission over a communication channel are affected by AWGN noise. However, in real environments, signals can be affected by other types of noise. In this way, we evaluate the performance of these techniques using four types of signals with different waveforms and synthetically add three types of noise: AWGN, sub-Gaussian noise, and super-Gaussian noise. In our experiments, WT was superior to the other techniques. It was evidenced visually and quantitatively with two indicators: Improved Signal-to-Noise (SNR) and Sample Entropy (SE). SE is not normally used to evaluate the denoising of signals, however, as we demonstrate in this work, it is more appropriate since it considers the level of distortion caused by denoising techniques. With the two indicators, the superiority of WT is demonstrated. In addition to this comparison, we apply the three techniques to signals measured in a real environment and show that an indicator like SNR is not suitable for evaluating performance. On the other hand, SE, in addition to indicating noise mitigation, has the characteristic of showing which technique distorts the processed signal to a lesser extent.