光学小波变换

首先讨论了常规傅里叶变换的缺点,导入短时傅里叶变换及小波变换,分析了小波变换的特点和实现小波变换的光学方案,在空域和频域中详细分析了利用高斯－哈尔小波变换进行边缘探测的特征,介绍了小波变换图形识别的结果。     

傅里叶变换的局限性及其改进方法

从对傅里叶变换的局限性分析入手 ,揭示了窗口傅里叶变换、小波变换和分数傅里叶变换的出现是傅里叶变换本身发展的必然 ,阐明了其改进方法产生的原因及其优缺点 ,分析了其改进方法与傅里叶变化的关系 ,这些有助于加深对傅里叶变换的认识。     

啁啾脉冲频域干涉仪相位重建方法的理论研究

理论研究了啁啾脉冲频域干涉仪的时域相移重建技术,对于接近实际的频谱干涉条纹,分别采用傅里叶变换和小波变换的方法完成了时域相位扰动信号的重建。傅里叶变换方法产生的重建误差受到滤波参数的影响,相对而言,小波变换方式解谱过程中,不需要进行特意的滤波操作,从而避免了重建结果存在误差不确定性的问题。     

小波相位解调轮廓术

针对傅里叶变换轮廓术因混频难以准确提取基频的问题,可将小波变换用于三维形貌相位直接解调。对其原理进行了研究,通过编程实现了小波相位解调。取Morlet复小波作为小波母函数,对调制栅线图逐行进行连续小波变换,从各位置的沿尺度方向的小波变换系数幅值的极值中可直接求取对应的相位数据。由于小波函数具有空域_频率两域的局部化特性,因此它对变形栅具有很强的自适应能力。为验证新方法,对其进行了仿真分析,同时还对石膏半球模型和化妆品瓶进行了实际测量,并分别用傅里叶变换和小波变换进行了处理。结果表明,新方法有效地克服了混频的问题,改善了相位解调效果,提高了测量精度,特别适合于复杂物体的形貌测量。     

小波变换轮廓术抑制CCD非线性的分析

对比研究了CCD非线性对小波变换轮廓术和傅里叶变换轮廓术的影响,并从信号频域角度分析推导出考虑CCD非线性时,变形条纹的小波变换的频谱描述形式,得到了"脊"处小波系数的解析表达式。处理由CCD非线性引起的非完善的条纹图时,采用小波变换轮廓术提取相位,实质是采用最佳的加权滤波窗口,这样能减弱CCD非线性引起的频谱混叠对测量的影响,可以得到比傅里叶变换轮廓术更稳定的恢复效果。计算机模拟验证了此结论的正确性。     

激光大气闪烁的小波频谱分析

激光对数光强起伏的快速傅里叶变换功率谱的无标度区间的标度指数在许多情况下很不稳定,并且超出了理论界限,因而本文引入了离散小波变换（ＤＷＴ）频谱分析。通过对１／ｆ信号的快速傅里叶变换频谱和离散小波换频谱的对比分析,验证了离散小波变换频谱分析的优越性。激光大气闪烁的离散小波变换频谱的无标度区间的标度指数在一天内（除日出后和日落前两段时间外）的变化比较稳定,并且超出理论界限。这此结果表明,对于一般在大气     

S变换轮廓术中消除条纹非线性影响的方法

S变换是短时傅里叶变换和小波变换的延伸和推广,是一种无损可逆的非平稳信号时频分析方法.它不仅具有线性、多分辨性和逆变换唯一性等特点,而且其反变换与傅里叶变换保持着直接的联系.在S变换中,以简谐波作为基波,以可以同时进行伸缩和平移的高斯函数作为窗函数.同短时傅里叶变换相比,S变换的时频分辨率可以同时达到最佳,同小波变换相...     

基于图像二维小波多尺度分解傅里叶变换轮廓术

应用傅里叶变换轮廓术测量物体三维面形时,当被测物体形状复杂或是被噪声严重污染时,导致频谱分布展宽,发生频谱混叠现象,基频提取困难,无法准确恢复物体的三维面型.提出了基于小波分解的傅里叶变换轮廓术,采用小波变换的方法对变形条纹图进行二维多尺度分解,重构被测物的背景图像,滤出图像的零频成分,得到相对变形条纹.运用小波变换与傅里叶变换轮廓术相结合的方法,只需拍摄一幅变形条纹图,将被测物体与背景分离,不受背景成分的影响,且易于基频信息的提取,降低了对滤波器的要求.实验证明该方法较好地防止了频谱的混叠问题,提高了测量范围与解相精度.     

基于小波变换的红外光谱分析

利用傅里叶变换红外光谱仪,借助OMNI采样器直接、快速、准确地测定了土茯苓及其三种伪品木质部的FTIR谱,采用小波变换分析法对样品进行了详细研究。结果表明：小波变换可以去除噪声和压缩变量,具有运算速度快、分析精度高以及无需去噪后处理等优点, 在红外光谱分析中具有很好的应用前景。     

基于连续小波变换FTIR鉴定青葙子及鸡冠子的研究

借助OMNI采样器,应用傅里叶变换红外光谱方法直接、快速、准确地测定青葙子及其伪品鸡冠子的红外光谱。利用连续小波变换对真伪品的红外光谱进行放大处理,以有效突出真伪品间的红外光谱差异程度,从而提高鉴定正确率。采用对信号奇异性具有良好探测能力的Morlet小波做小波母函数,对青葙子真伪品的红外光谱进行若干尺度的一维连续小波变换,在各个尺度下观察青葙子的真伪品的红外光谱的差异程度,从中选择一个差异程度最为明显的尺度来区分青葙子真伪品。结果表明：基于连续小波变换的傅里叶红外光谱分析方法能够有效鉴别同科同属不同种植物中药材。     

三维测量中一种新的自适应窗口傅里叶相位提取法

针对多尺度窗口傅里叶变换中,窗口尺寸的自适应选取及提取基频时的频谱混叠等问题,提出基于希尔伯特-黄变换(HHT)的自适应窗口傅里叶相位提取法。对变形条纹信号进行HHT后,通过谱分析,自适应确定能够准确描述条纹信号变化情况的瞬时频率及条纹图的背景分量。根据所得的瞬时频率,给出自适应定位条纹信号局部平稳区域的步骤,进而确定窗口尺寸。不需额外计算,可有效去除背景分量以减少基频提取过程中零频频谱的干扰。与现有的用最大脊法确定窗口尺寸的方法相比,本方法不受被测相位必须线性逼近且变化缓慢的前提约束。实验证明本方法有效、可行,且对测量携带陡峭边缘或面形复杂的物体也能进行较为精确有效的测量。     

The time-singularity multifractal spectrum distribution

Although the multifractal singularity spectrum revealed the distribution of singularity exponent, it failed to consider the temporal information, therefore it is hard to describe the dynamic evolving process of non-stationary and nonlinear systems. In this paper, we aim for a multifractal analysis and propose a time-singularity multifractal spectrum distribution (TS-MFSD), which will hopefully reveal the spatial dynamic character of fractal systems. Similar to the Wigner–Ville time-frequency distribution, the time-delayed conjugation of fractal signals is selected as the windows function. Furthermore, the time-varying Holder exponent and the time-varying wavelet singularity exponent are deduced based on the instantaneous self-correlation fractal signal. The time-singularity exponent distribution i.e. TS-MFSD is proposed, which involves time-varying Hausdorff singularity spectrum distribution, time-varying large deviation multifractal spectrum and time-varying Legendre spectrum distribution, which exhibit the singularity exponent distribution of fractal signal at arbitrary time. Finally, we studied the algorithm of the TS-MFSD based on the wavelet transform module maxima method, analyzed and discussed the characteristic of TS-MFSD based on Devil Staircase signal, stochastic fractional motion and real sea clutter.     

提升小波变换与分形相结合的图像压缩

提出了一种提升小波变换与分形相结合的图像压缩方案.充分利用小波变换后系数能量的分布特性,对提升小波变换后的低频部分采用改进的分形图像压缩编码,其余部分采用集合分裂嵌入块(SPECK)编码算法.试验结果表明,该方法在提高了压缩效率的同时,获得了较高的恢复图像质量.     

Intensity analysis methods for transient signals

Conventionally, the Fourier transform is applied for sound intensity analysis of stationary signals, but this method can be applied for analyzing non-stationary transient signals. Instead of the Fourier transform analysis, instantaneous spectrum analysis methods such as the Wigner-Ville distribution and the wavelet transform are proposed. By using the mathematical example as a transient signal, advantages and disadvantages of these methods including the short-time Fourier transform are compared. From calculation results, it is considered that the STFT method is the most suitable for the accurate measurement of sound intensity levels, but the WT method is also recommended from its higher resolution of transient signals.     

Evaluation of spectral phase in spectrally resolved white-light interferometry: Comparative study of single-frame techniques

Spectral phase in a white-light interferogram contains information about the absolute optical path difference (OPD) in the interferometer. Evaluation of spectral phase is therefore important in applications such as profilometry with white light. In spectrally resolved white-light interferometry (SRWLI) the white-light interferogram is spectrally decomposed by a spectrometer in order to determine this phase. Several single-frame techniques in SRWLI have been proposed for the evaluation of the phase including Fourier transform, Hilbert transform, spatial phase shifting, windowed Fourier transform and wavelet transform. In this paper we present a comparative study of these techniques in this application in relation to the temporal phase-shifting technique which is a multi- frame method. Further, we also propose a modified method to remove the influence of source spectrum modulation in Hilbert transform procedure.     

Extended fractional wavelet joint transform correlator

An extended fractional wavelet joint transform correlator is implemented for real-time target recognition applications. The real-time input scene captured using a charge-coupled device camera along with the reference image is fractional Fourier transformed. The obtained joint power spectrum is multiplied by an appropriately scaled wavelet filter and the resultant function is differentiated. The application of wavelet filter enhances the correlation outputs and differential processing of wavelet-filtered joint power spectrum improves the detection efficiency by reducing the zero-order spectra. Targets with Gaussian and speckle noise have also been used to check the correlation output. The performance metrics: correlation peak intensity, peak-to-correlation energy, peak-to-sidelobe ratio and signal to clutter ratio have been calculated. The experimental results are presented in support of the proposed idea.     

子波变换在光信息处理方面的应用

子波变换是光信息处理中的一个重要工具，与常用的傅里叶交换和Ｇａｂｏｒ变换相比，在分析瞬态信号方面有很多优点。此文详细介绍子波变换的基本原理以及如何用光学方法实现子波变换，揭示其在光信息处理方面的应用前景。