Time Series Denoising based on Wavelet Decomposition and Cross-Correlation between the Residuals and the Denoised Signal

In this paper, a new denoising method, based on the wavelet transform of the noisy signal, is described. The method implements a variable thresholding, whose optimal value is determined by analyzing the cross-correlation between the denoised signal and the residuals and by applying different criteria depending on the particular decomposition level. The residuals are defined as the difference between the noisy signal and the denoised signal. The procedure is suitable for denoising signals in real situations when the noiseless signal is not known. The results, obtained with synthetic data generated by well-known chaotic systems, show the very competitive performance of the proposed technique.