Research On The Application Of Wavelet Technique In The Signal Reconstruction And De-Noising

Wavelet analysis developed from Fourier analysis is a new time-frequency analysis tool which has favorable time-frequency localized and multi-resolution properties. Wavelet analysis has been widely applied in signal processing field and other fields. In this paper, a fast signal reconstruction algorithm and a signal de-noising algorithm from its wavelet transform modulus maxima are presented.The wavelet transform modulus maxima have close affiliation with the singular points of signals. It has been used in many fields, including signal de-noising, edge detection, data compact, pattern recognition etc. How to reconstruct the original signal from the wavelet transform modulus maxima is a key issue. In this paper, the relationship between the modulus maxima and wavelet transform coefficients has been analyzed, and by adding a new interpolation point between the adjacent modulus maxima with the same sign, a reconstruction algorithm based on monotone piecewise cubic Hermite interpolation has been put forward. This reconstruction algorithm has explicit physical meaning. Compared with Mallat algorithm and the cubic spline interpolation algorithm, this algorithm has less complex and can be implemented conveniently. It is high practicability.In the process of signal collection, transform and transmission, the signal often mix noise ineluctably because the equipments, environments and even human errors. De-noising with the purpose of extracting desired information has been a crucial technique in signal processing. In this paper, the signal de-noising problem based on wavelet transform modulus maxima is discussed. According to the different characters of wavelet transform modulus maxima of signal and noise, a de-noising algorithm based on wavelet transform modulus maxima is proposed. The experimental results show that this method is efficient and practical.Based on the properties of wavelet transform and the statistical characteristics of noise, Donoho presented the threshold de-noismg in wavelet transform domain. By selecting appropriate threshold and threshold function, the noise can be suppressed. But there are discontinuity of hard-threshold function and biased estimation of soft-threshold function. In this paper, a new threshold function which overcomes the inherent disadvantages of hard-threshold and soft-threshold is proposed. In addition, a local multi-threshold selection method is put forward. Experiments show that the improved method has better performance of de-noising than the traditional methods.In short, the proposed signal reconstruction algorithm based on piecewise monotone cubic Hermite function interpolation has been proved to have better results. The new threshold de-noising algorithm can reach the expected outcome and has good stability and reliability.