Research on signal de-noising methods based on the convolution type of wavelet packet transformation

Abstract

A multi-scale de-noising algorithm based on the con-volution type of wavelet packet transformation is presented. This algorithm overcomes the shortcoming that the length of sequences obtained always decreases with the decomposition scales increasing. The new algorithm improves noise variance estimation methods and keeps the main edges of signal well. A new thresholding function is employed, which is simple in expression and as continuous as the Donohopsilas soft-thresholding function. Moreover, this function overcomes the shortcoming that an invariable dispersion between the estimated wavelet coefficients and the decomposed wavelet coefficients in the soft-thresholding method. Simulation results indicate that this method suppresses the Pseudo-Gibbs phenomena effectively and achieves better SNR gains.