Determination of the threshold and the decomposition order in threshold de-noising method based on wavelet transform

Threshold de-noising method based on wavelet transform is an efficient method to reduce the white noise in the digital signal. There are two key problems that need to be solved in practice use of this non-linear filter method. One is the determination of the threshold; another is the determination of the decomposition order. The necessity of determining a proper decomposition order is proved through digital simulation. The characteristics of the wavelet coefficients of useful signal polluted by white noise are analyzed. A new method is proposed to determine the decomposition order adaptively, and then a novel method based on the 3σ rule is brought forward to determine the threshold of each order of wavelet space. Simulation results show that the method has good performance. It is especially suitable for the detection of faint signal under strong noise background. The methods of determining the two important parameters are proposed explicitly, and this will improve the practicability of threshold de-noising method based on wavelet transform in project use.