匹配小波构造方法及其应用研究
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摘要
小波变换由于具有良好的时频局部特性,已成为处理非平稳信号的有力工具,小波理论和设计受到了广泛的关注。有学者指出:“在小波分析的理论研究和应用中,存在着两个关键性的理论问题:第一个问题是小波的构造问题;第二个问题是如何根据信号的特点和信号处理的需要,自适应选取最优小波基的问题”。如何选取小波基,一直是小波理论与应用研究领域的重要问题之一。本文在探讨了小波变换理论的基础上,力图将匹配、时变与小波相结合,对最优匹配小波和时变匹配小波的理论与设计方法进行了深入研究。论文的主要研究工作包括:基于能量匹配的最优匹配小波设计,并将它应用于信号消噪与压缩中,基于格结构的时变匹配小波设计,基于匹配小波的主动式回波探伤系统。
主要工作概述如下:
(1)研究匹配小波的设计算法有助于提高小波在实际应用中的性能。本文在讨论了小波与信号匹配方式的基础上,提出了最优小波匹配准则,给出了相应的构造与设计算法,该方法根据信号在尺度空间最大投影原则,利用满足正则条件的结构化完全重构滤波器组和优化算法,构造了具有一定正则性的小波滤波器组,实现了尺度空间系数重构信号与给定信号的误差最小。其次,设计了与超声回波信号匹配的小波滤波器组,结果表明,最优匹配小波能够获得最佳的信号表示。
(2)近年来,越来越多的学者对时变滤波器组进行了理论及设计方面的研究,但还存在许多未解决的问题,不论是时域还是频域,还没有通用的设计方法;有许多领域,时变滤波器组,时变小波都未涉及。本文阐述了基于格结构的时变滤波器组,根据匹配准则和小波的特定条件,利用优化目标函数,提出时变匹配小波的设计方法,建立相应的理论及设计体系。仿真和实验信号验证了方法的有效性,尤其是在时变信号含噪的情况下,也能有效地将信号分离和提取出来。表明时变匹配小波在处理时变信号时要优于其它小波。
(3)在信号压缩和消噪应用中,小波基的选择直接影响着处理效果。本文针对超声回波和图像,研究了用于消噪的小波与信号和图像的匹配原则,在采用能量匹配原则的基础上,分别探讨了应用最优匹配小波对超声回波和图像消噪的方法,并取得令人满意的效果。其次将最优匹配小波应用于心电信号和图像压缩,利用结构化小波滤波器组以及新的波形匹配准则,选用与信号波形最优相似的
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.
主要工作概述如下:
(1)研究匹配小波的设计算法有助于提高小波在实际应用中的性能。本文在讨论了小波与信号匹配方式的基础上,提出了最优小波匹配准则,给出了相应的构造与设计算法,该方法根据信号在尺度空间最大投影原则,利用满足正则条件的结构化完全重构滤波器组和优化算法,构造了具有一定正则性的小波滤波器组,实现了尺度空间系数重构信号与给定信号的误差最小。其次,设计了与超声回波信号匹配的小波滤波器组,结果表明,最优匹配小波能够获得最佳的信号表示。
(2)近年来,越来越多的学者对时变滤波器组进行了理论及设计方面的研究,但还存在许多未解决的问题,不论是时域还是频域,还没有通用的设计方法;有许多领域,时变滤波器组,时变小波都未涉及。本文阐述了基于格结构的时变滤波器组,根据匹配准则和小波的特定条件,利用优化目标函数,提出时变匹配小波的设计方法,建立相应的理论及设计体系。仿真和实验信号验证了方法的有效性,尤其是在时变信号含噪的情况下,也能有效地将信号分离和提取出来。表明时变匹配小波在处理时变信号时要优于其它小波。
(3)在信号压缩和消噪应用中,小波基的选择直接影响着处理效果。本文针对超声回波和图像,研究了用于消噪的小波与信号和图像的匹配原则,在采用能量匹配原则的基础上,分别探讨了应用最优匹配小波对超声回波和图像消噪的方法,并取得令人满意的效果。其次将最优匹配小波应用于心电信号和图像压缩,利用结构化小波滤波器组以及新的波形匹配准则,选用与信号波形最优相似的
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.
引文
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