De-noising by Self-Adaptive Lifting Algorithm Based on Modulus Maximum Analysis

De-noising by the traditional wavelet transform, the result is affected by the choosing of wavelet base. Because the wavelet base is fixed in the traditional wavelet transform, either the smoothness or singularity of the signal canpsilat be fitted quite well. To overcome the limitation, a new self-adaptive lifting scheme based on modulus maximum analysis is presented. Modulus maximum sequence of the large scale wavelet coefficients can locate the point of the signal with big singularity precisely. According to the position of the point with big singularity, proper neighborhood is fixed, and prediction operator can be chosen self-adaptively. In this way, the prediction operator is fitted to the local feature of the signal. The simulation and engineering application showed that the proposed method could overcome the de-noising disadvantage of traditional wavelet transform. It not only can filter noise from original signal effectively but also can hold local characteristics of original signal in the de-noised signals.