Study Of Matched Wavelet Construction Methods And Their Applications

Compared with Fourier transform, wavelet transform has better ability to analyze the singularities and irregular signal because of a multi-resolution analysis, and we can obtain the details of signal at different scales by applying a wavelet transform. A chronological development of efforts in wavelet analysis shows that WT is a good tool for analyzing the non-stationary signal. The given signal projects into the basis function of wavelet, each of which is a dilation and translation of a function called mother waveletψ(t), at diffirent scale. Unlike FT, WT do not have a unique basis. Using different basis function of wavelet to analyze signal will get different results. If we design the wavelet to match the signal to be analyzed, the best representation of the signal can be resulted. Usually, one uses a wavelet to do signal decomposition; it is something like a blind man's walk. If we know the particular features of the signal and then design a wavelet to match the signal, it would be better. This is a reason that matched wavelets are finding applications in diverse fields and is a topic of current research. The main contents conclude: a method for construction of best matched wavelet, construction of orthogonal matched time-varying wavelet; denoising and compression based on optimal matched wavelet for echo and image; a new approach for ultrasound echo detection based on best matched wavelet. Many new algorithms and strategies are proposed for different problems, and can be summarized as follows:(1) This paper proposed an approach which is based on structural filter bank of wavelet for constructing matched wavelet. The method is to find the maximal projection of the given signal on the scaling subspace. Two kinds of wavelet filter banks based on this algorithm are constructed. The optimal algorithm of the matched wavelet is presented. The new method over existed methods has low design complexity and can directly obtain wavelet filter bank. Two examples are also presented and the errors between original and reconstruction signal are obtained. It is shown that the results of error by matched wavelet are reduced.(2) Time-Varying Wavelet is a good tool for analyzing non-stationary signal. The main problem for the construction of the time-varying filter is how to satisfy the condition for perfect reconstruction (PR) and regularity. This paper proposed a technique for constructing a time-varying wavelet based on the lattice structures of two-channel perfect-reconstruction quadrature filter banks, satisfying the PR condition. Firstly, the property of perfect-reconstruction and orthogonal is guarantied from structure. Secondly, the lattice coefficient having the regularity is given, while the optimization algorithm ensures implementation of the matched time-varying wavelet filter banks. This method is constructive and is used to generate time-varying orthogonal wavelet based on lattice structure, the application of time-varying matched wavelet denoising time-varying signal is also presented. Simulation shows that the proposed algorithm for constructing time-varying matched wavelet is efficient in time-varying signal procedure. Therefore, the time-varying matched wavelet is superior to the other time-varying wavelet in processing time-varying signal.(3) Wavelet transform is widely used in data compression and denoising. How to choice the best wavelet base is a key point for improving the compression ratio and SNR. In this paper, we put forward a idea of using wavelet base functions matching to signal. Firstly, We deal with denoising by using optimized match wavelet transform for ultrasonic echo and image. Some simulation results are given and they show that the effect by matched wavelet is superior to that by non-match wavelet in SNR enhancement. Secondly, a waveform matching criteria for contructing matched wavelets is given. The wavelet filter is constructed with an structure filter banks and the criteria, and two examples of compressing two-dimension image are presented. Compared with other wavelet filters, the matched wavelet filter is able to improve the performance of signal compression and denoising .(4) Detection of flaw echoes in the presence of high scattering microstructure noise is an important issue in ultrasonic nondestructive evaluation (NDE). As an efficient time-frequency analysis tool, the wavelet transform (WT) has been widely used to improve ultrasonic flaw detection performance. However, those wavelet-based methods usually can not guarantee the wavelet matching the flaw echo in a good way, thus the detection performance can not be improved distinctly. This paper proposed an novel method for detecting echo signals. The wavelet function is used as the transmit signal and the echo signal is detected with the corresponding completely same wavelet base. So the best match can be arrived. The advantage and implementation of new method was described. The simulation of the ultrasonic detection indicates the validity of the new way. The numerical results show good detection even for SNR of -17dB. Comparing with traditional method, the new method can increase the ability of signal detection.