Signal De-noising Research Based On Wavelet Transformation

Wavelet transform is a new-style mathematic analysis tool. It is a new subject which was rapidly developed in late 1980s. The wavelet transform has the characteristic of multi-analysis and the ability to analyse partial characteristic both in the time domain and the frequency range, so it is suitable to analyze non-steady state signal and observe signal gradually from coarse to fine. The method has been used in many domains such as signal processing, image processing, pronunciation distinction, pattern recognition, quantum physics and so on. It is considered as a great breakthrough of tools and methods recently.It is inevitable to be interfered by a large amount of noise signal in the process of signal gathering and transmission. It's a main topic to deniose and extract original signal. In practice, Donoho's hard-thresholding and soft-thresholding algorithm is frequently used to denoising and has obtained a good effect. Discontinuity of the hard-thresholding function results in pseudo-Gibbs phenomenon of the reconstructed signal. Soft-thresholding function has good continuity but a constant deviation of the estimated value from the actual value confines its application. Thereafter all papers of this subject were centered on making some improvements based on Donoho's thresholding method and made certain success in improving the ratio of signal to noise and denoising. In order to obtain better denoising, not only appropriate wavelet function but also the best decomposition layer must be choosed and the appropriate thresholding should be determined.The selection of thresholding affects final denoising effect directly. It's difficult to remove the noise and reserve the primitive signal simultaneously in signal denoising. If the thresholding is too low, the denoising will be insufficient. If thresholding is too high, some weak signal will be taken as noise and denoised wrongly .Thresholding should be selected according to levels of signal.According to the definition of wavelet transform and the different characteristic of signal and the noise, a new thresholding function is proposed based on the analysis of the advantage and disadvantage of various denoising algorithms. The new threshold function has many advantages over hard-thresholding and soft-thresholding functions. It has good continuities and high-order derivatives and is convenient to treat mathematically. A novel denoising algorithm based on the new thresholding function is proposed to remove white noise mixed in one-dimensional steady signal. The white noise mixed in pronunciation signal can be effectively removed by using the algorithm and the usability and versatility is very good. The algorithm is also suitable for denoising of pronunciation signal. By using the algorithm,the white noise in which the voice signal contain can be so effectively removed that the SNR and the identifiability are greatly improved. Another denoising algorithm based on wavelet transform is proposed for two dimensional image signal processing. And by using the algorithm the white noise mixed in image signal can be effectively removed and the definition and identifiability of images can be greatly enhanceed. Denoising algorithm based on wavelet packet transform is also researched and the algorithm is for fingerprint image and the denoising effect is very satisfactory.