A novel fractional wavelet transform and its applications

The wavelet transform (WT) and the fractional Fourier transform (FRFT) are powerful tools for many applications in the field of signal processing.However,the signal analysis capability of the former is limited in the time-frequency plane.Although the latter has overcome such limitation and can provide signal representations in the fractional domain,it fails in obtaining local structures of the signal.In this paper,a novel fractional wavelet transform (FRWT) is proposed in order to rectify the limitations of the WT and the FRFT.The proposed transform not only inherits the advantages of multiresolution analysis of the WT,but also has the capability of signal representations in the fractional domain which is similar to the FRFT.Compared with the existing FRWT,the novel FRWT can offer signal representations in the time-fractional-frequency plane.Besides,it has explicit physical interpretation,low computational complexity and usefulness for practical applications.The validity of the theoretical derivations is demonstrated via simulations.     

一种新型分数阶小波变换及其应用

小波变换和分数Fourier变换是应用非常广泛的信号处理工具.但是,小波变换仅局限于时频域分析信号;分数Fourier变换虽突破了时频域局限能够在分数域分析信号,却无法表征信号局部特征.为此,提出了一种新型分数阶小波变换,该变换不但继承了小波变换多分辨分析的优点,而且具有分数Fourier变换分数域表征功能.与现有分数阶小波变换相比,新型分数阶小波变换可以实现对信号在时间-分数频域的多分辨分析.此外,该变换具有物理意义明确和计算复杂度低的优点,更有利于满足实际应用需求.最后,通过仿真实验验证了所提理论的有效性.     

一种新的基于主分量变换与小波变换的图像融合方法

为了更好地进行不同分辨率图像的融合,提出了一种基于主分量变换与小波变换结合的多光谱图像与高分辨率图像融合方法。该新方法首先对多光谱图像进行主分量变换;然后分别对其第1主分量与高分辨率图像进行小波变换,并采用成像强度对比法有效地将经小波分解的高分辨率图像的低频分量信息融合到经小波分解的多光谱图像的第1主分量的低频分量中;最后,通过将小波融合结果作为多光谱图像的第1主分量再做逆主分量变换来得到最终的融合图像。实验结果分析表明,该新方法使融合图像在较好地保留光谱信息的同时,空间细节信息也得到了增强,比典型的IHS变换、主分量变换及小波变换融合方法具有更好的融合效果。     

基于小波的信号突变点检测算法研究

本文利用小波多分辨分析的特性将突变信号进行多尺度分解,然后通过分解后的信号来确定突变信号的突变位置。Lipschitz指数被用来定量描述函数的奇异性。当小波变换尺度越来越精细时,小波变换模极大值信号突变点的衰减速度取决于信号在突变点的Lipschitz指数。小波变换不仅可以确定突变点发生的时间,而且可以进一步判断突变的性质。     

基于小波的信号分析

简介小波概念之后,对一组模拟信号进行分析,采用小波变换,选出合适的小波函数,处理后再重构。对采用Mexican hat小波、Shannon小波、Meyer小波这三种不同小波得到的去噪结果进行比较,验证信号的滤波效果与选取的小波类型有较大的关系。     

基于Radon和解析Fourier-Mellin变换的尺度与旋转不变目标识别算法

由于正交矩对噪声鲁棒性强、重建效果好,因此被广泛应用于目标识别与分类中,但是正交矩本质上缺乏尺度变换不变性,而且必要的图像二值化与规一化过程会引入重采样与重量化误差。为此,在研究现有正交矩的基础上,提出了一种基于Radon变换和解析Fourier-Mellin变换的尺度与旋转不变的目标识别算法。该算法首先直接对目标灰度图像进行Radon变换,然后对Radon变换结果进行进一步解析,通过Fourier-Mellin变换将原图像的旋转变化转化为相位变化,将原图像的尺度变化转化为幅度变化;最后,通过定义一旋转与尺度不变函数,同时利用不变函数的4种特征,再应用k-近邻法实现分类。理论与实验结果表明,由于避免了正交矩方法存在的重采样与重量化误差,该算法的分类精度高于基于正交矩的分类方法,而且对白噪声的鲁棒性也显著高于基于正交矩的识别与分类方法。     

基于Contourlet变换的遥感影像融合算法

针对目前最新发展的Contourlet变换能比小波变换更适合于进行多尺度边缘增强处理的特点，本文提出了一种新的基于Contourlet变换的用于融合遥感全色和多光谱影像的算法，分别对应于Contourlet变换后得到的低频和高频分量系数，结合小波变换采用了不同的融合规则．实验结果表明本文提出的融合算法能在保留多光谱影像光谱信息的同时增强了融合图像的空间细节表现能力和信息量，该算法是有效可行的．     

数字图像压缩中的域变换技术

该文讨论了数字图像压缩中三种具有代表性的图像变换方法,并采用C 程序语言验证这几种方法。     

数字图像压缩中的域变换技术

该文讨论了数字图像压缩中三种具有代表性的图像变换方法，并采用C＋＋程序语言验证这几种方法。     

基于Radon和解析Fourier Mellin变换的尺度

由于正交矩对噪声鲁棒性强、重建效果好,因此被广泛应用于目标识别与分类中,但是正交矩本质上缺乏尺度变换不变性,而且必要的图像二值化与规一化过程会引入重采样与重量化误差。为此,在研究现有正交矩的基础上,提出了一种基于Radon变换和解析FourierMellin变换的尺度与旋转不变的目标识别算法。该算法首先直接对目标灰度图像进行Radon变换,然后对Radon变换结果进行进一步解析,通过FourierMellin变换将原图像的旋转变化转化为相位变化,将原图像的尺度变化转化为幅度变化;最后,通过定义一旋转与尺度不变函数,同时利用不变函数的4种特征,再应用k近邻法实现分类。理论与实验结果表明,由于避免了正交矩方法存在的重采样与重量化误差,该算法的分类精度高于基于正交矩的分类方法,而且对白噪声的鲁棒性也显著高于基于正交矩的识别与分类方法。     

The Two-Dimensional Clifford-Fourier Transform

Recently several generalizations to higher dimension of the Fourier transform using Clifford algebra have been introduced, including the Clifford-Fourier transform by the authors, defined as an operator exponential with a Clifford algebra-valued kernel. In this paper an overview is given of all these generalizations and an in depth study of the two-dimensional Clifford-Fourier transform of the authors is presented. In this special two-dimensional case a closed form for the integral kernel may be obtained, leading to further properties, both in the L ₁ and in the L ₂ context. Furthermore, based on this Clifford-Fourier transform Clifford-Gabor filters are introduced. AMS subject classification numbers: 42B10, 30G35 Fred Brackx received a diploma degree in mathematics from Ghent University, Belgium, in 1970 and a Ph.D. degree in mathematics from the same university in 1973. Since 1984 he is professor for mathematical analysis at Ghent University and currently he is leading the Clifford Research Group. His main interests are function theory and functional analysis for functions with values in quaternion and Clifford algebras. The research covers Clifford distributions, generalized Fourier, Radon and Hilbert transforms, orthogonal polynomials and multi-dimensional wavelets. Nele De Schepper received a diploma degree in mathematics from Ghent University, Belgium, in 2001. Since then she holds an assistantship at the Department of Mathematical Analysis of Ghent University and is a member of the Clifford Research Group. Her main interests are function theory and functional analysis for functions with values in Clifford algebras. The research covers generalized Fourier transforms, orthogonal polynomials and multi-dimensional wavelets. Frank Sommen received a diploma degree in mathematics from Ghent University, Belgium, in 1978, a Ph.D. degree in mathematics from the same university in 1980, and a habilitation degree in mathematical analysis in 1984. From 1978 until 1999 he was at the National Fund for Scientific Research (Flanders). Since 2000 he holds a Research professorship at Ghent University. His main interests are function theory and functional analysis for functions with values in quaternion and Clifford algebras. The research covers Clifford distributions, generalized Fourier, Radon and Hilbert transforms, orthogonal polynomials and multi-dimensional wavelets, algebraic analysis, hyperfunctions and radial algebra.     

分数阶小波变换的性质

小波变换是对信号时域-频域(Fourier域)的多分辨率分析,是一种线性时不变伸缩带通滤波.分数阶小波变换将小波变换的多分辨率分析理论推广到时域-广义频域(分数阶Fourier域),对信号分析处理有更大的灵活性.分析了分数阶小波变换的线性时变特性、存在正交分教阶小波的条件、分数阶Fourier域传递函数,以及分数阶小波变换在分数阶Fourier域的伸缩带通滤波.     

分数阶小波变换

小波变换是对信号时域-频域(Fourier域)的多分辨率分析,也可看作是一种Fourier域伸缩带通滤波.分数阶Fourier变换是对传统Fourier变换的推广,对信号分析处理有更大的灵活性,为了将多分辨率分析理论推广到时域-广义频域(分数阶Fourier域),提出了一种分数阶小波变换,分析了分数阶小波变换在广义频域伸缩带通滤波特性,分析信号时的时域-广义频域平面的多分辨率分析网格划分.分数阶小波变换是传统小波变换的推广,在对原小波变换核作一定改动后增加了小波变换对信号处理的灵活性.可以看到,将分数阶小波变换的变换角度取为π/2,便得到与传统小波变换多分辨率分析理论完全一致的结果.理论分析和计算机仿真表明了所提理论的正确性和有效性.     

A novel license plate location method based on wavelet transform and EMD analysis

Although various license plate location methods have been proposed in the past decades, their accuracy and ability to deal with different types of license plates still need to be improved. A robust license plate location method can raise the accuracy of the whole license plate recognition procedure. This paper proposes a robust method based on wavelet transform and empirical mode decomposition (EMD) analysis to search for the location of a license plate in an image to deal with some challenging problems in practice such as illumination changes, complex background and perspective change. By applying wavelet transform on a vehicle image and projecting the acquired details of the image, a wave crest that indicates the license plate will be generated. In order to locate the desired wave crest in the nonlinear and non-stationary projection dataset, EMD analysis is applied. Using the reconstructed projection data and the Hilbert transform of intrinsic mode function components, the position of the license plate is detected. Comprehensive experiments show that this method can locate the positions of various types of license plates with a high accuracy of 97.91% and a relatively short running time.     

多分辨率形态学目标检测

用形态小波变换得到图像的塔式表示,并从最低分辨率到原始分辨率由粗到精地提取目标区域.在每个分辨率上,先应用分水岭变换分割该分辨率下的低频分量（或上一级分辨率得到的标记图）,得到一个标记图;再用一个区域搜索策略来更新该标记图.对多类目标的实验结果验证了该算法具有速度快、精度高和对噪声不敏感的优点.     

一种基于小波变换的分形图像编码压缩算法的研究

有效的编码压缩算法是图像数据存储和传输的关键。本文在分析基本分形编码压缩算法(FCC)优缺点的基础上，提出了一种新的结合小波变换的分形图像编码压缩算法(DWT—FCC)，该算法首先对图像进行二级小波变换分解，然后对分解后的高层子图像进行基本分形编码，并根据不同层子图像结构间的相似性，由高层分形编码构造低层子图像分形编码，实现图像的编码压缩。实验结果表明，该算法在缩短图像编码时间和提高压缩比方面，均取得了良好的效果。     

基于IHS变换与小波变换的遥感图像融合

针对多光谱图像与全色图像的融合，本文提出了一种基于IHS变换和小波变换的遥感图像融合方法。新方法首先对多光谱图像作IHS变换，得到亮度I，色度H，饱和度S三个分量；其次，利用小波变换融合方法融合多光谱图像的亮度分量与全色图像，并用融合后的图像替代多光谱图像的亮度分量；最后，作IHS反变换得到新的多光谱图像。主观视觉效果分析和客观统计参数评价分析表明，新方法的性能优于IHS变换融合方法、小波变换融合方法和PCA变换融合方法，不仅较大地增强了融合图像的空间细节表现能力，而且很好地保留了多光谱图像的光谱信息。     

Bias Error Analysis of the Generalised Hough Transform

The generalised Hough transform (GHT) extends the Hough transform (HT) to the extraction of arbitrary shapes. In practice, the performance of both techniques differs considerably. The literature suggests that, whilst the HT can provide accurate results with significant levels of noise and occlusion, the performance of the GHT is in fact much more sensitive to noise. In this paper we extend previous error analyses by considering the possible causes of bias errors of the GHT. Our analysis considers both formulation and implementation issues. First, we compare the formulation of the GHT against the general formulation of the standard HT. This shows that, in fact, the GHT definition increases the robustness of the standard HT formulation. Then, in order to explain this paradoxical situation we consider four possible sources of errors that are introduced due to the implementation of the GHT: (i) errors in the computation of gradient direction; (ii) errors due to false evidence attributed to the range of values defined by the point spread function; (iii) errors due to the contribution of false evidence by background points; and (iv) errors due to the non-analytic (i.e., tabular) representation used to store the properties of the model. After considering the effects of each source of error we conclude that: (i) in theory, the GHT is actually more robust than the standard HT; (ii) that clutter and occlusion have a reduced effect in the GHT with respect to the HT; and (iii) that a significant source of error can be due to the use of a non-analytic representation. A non-analytic representation defines a discrete point spread function that is mapped into a discrete accumulator array. The discrete point spread function is scaled and rotated in the gathering process, increasing the amount of inaccurate evidence. Experimental results demonstrate that the analysis of errors is congruent with practical implementation issues. Our results demonstrate that the GHT is more robust than the HT when the non-analytic representation is replaced by an analytic representation and when evidence is gathered using a suitable range of values in gradient direction. As such, we show that errors in the GHT are due to implementation issues and that the technique actually provides a more powerful model-based shape extraction approach than has previously been acknowledged.     

一种基于小波包变换的遥感影像融合方法

针对多光谱遥感影像和全色遥感影像,提出了一种基于小波包变换的遥感影像融合方法。新方法首先对多光谱遥感影像进行PCA变换;其次对多光谱遥感影像的第一主分量和全色遥感影像进行小波包变换;然后保留多光谱影像第一主分量的低频近似分量,融合它们的高频细节分量;最后,做小波包反变换,得到新的多光谱遥感影像第一主分量,再做PCA反变换,得到新的多光谱遥感影像。与PCA变换融合方法、IHS变换融合方法和小波变换融合方法等方法在主观视觉效果分析和客观统计参数两方面做了比较,新方法是有效的,不仅较大地增强了结果影像的空间细节表现能力,而且很好地保留了多光谱影像的光谱信息。     

结合伽马变换和小波变换的PCA人脸识别算法

为了有效地提取人脸特征,提出了一种在传统PCA算法的基础上,结合伽马变换与小波变换的人脸识别算法。该方法对人脸图像进行伽马变换,消除光照等非线性因素的影响;对变换后的人脸图像进行小波分解,用得到的低频分量来替代原始人脸;对得到的人脸低频分量作PCA特征提取,得到最终的鉴别特征。在ORL人脸库上进行测试,该算法的识别率比传统的PCA算法提高了6.5%。