An adaptive wavelet transform based on lifting scheme and its application

In order to overcome the limitation of the classical wavelet transform, an adaptive wavelet transform denoising method was proposed which uses the correlation between samples to detect features of signal. On the basis of the lifting scheme wavelet transform, several sets of predictors and updaters are prepared in the transform. Local features of the signal on each level were examined by using the correlation between the transforming sample and its neighbors. According to the magnitude of the correlation factors, an optimal predictor and an optimal updater were chosen for the transforming sample. The simulation experiments and engineering application showed that the proposed method can overcome the defect of classical wavelet denoising method that may lose some local information of the original signal. The present method can not only remove noise from the original signal effectively, but also retain the local information of the original signal.