小波变换的计算机实现

小波变换是傅里叶变换的改进,在工程领域中得到了广泛应用。本文主要结合MATLAB介绍小波变换的计算机实现,包括三种类型的小波变换。文中首先介绍了连续小波变换的数值积分实现,接着介绍了多分辨率分析和Mallat算法,最后用滤波器组实现了离散网格上的小波变换和离散序列的小波变换。     

一个基于C语言的小波变换的图像压缩方案

本文简单介绍了小波变换的基本原理,并且结合小波变换介绍了一种基于C语言的小波变换的图像压缩方法.     

基于平稳小波的X射线底片数字图像去噪方法研究

本文介绍了小波变换的基本内容,重点介绍了离散小波变换和平稳小波变换,并采用平稳小波变换对X光底片进行处理,将平稳小波与离散正交小波进行了对比实验。实验结果证明,利用平稳小波去噪具有较好的视觉效果,提高了被检对象缺陷的辨识率。     

Fourier变换和小波变换一般形式 —线调频小波变换和多普勒小波变换

Fourier变换、窗口Fourier变换与小波变换在许多领域得到广泛的应用。该文回顾了Fourier变换和小波变换的发展;介绍了两种新的处理非平稳信号的方法,即线调频小波变换和多普勒小波变换;分析了线调频小波变换是短时Fourier变换和小波变换的时频分析的统一时频表示形式,Fourier变换、小波变换以及线调频小波变换都是多普勒小波变换的特殊情况。线调频小波变换和多普勒小波变换比Fourier变换和小波变换更具灵活性,为图像、信号处理提供了新的方法和工具。     

小波变换理论应用进展

本文介绍了小波变换理论,讨论了基本小波函数的选取准则和小波变换算法,分析了小波变换与人工智能等其它方法的结合方式和特点.通过介绍小波变换在信号瞬态分析、图像边沿检测、图像去噪、模式识别、数据压缩、分形信号分析等方面的应用实例,讨论了小波变换在处理非平稳信号和复杂图像时的优势.最后,对小波变换理论的发展及其应用前景作了描述.     

基于二维小波变换的图像压缩的算法研究

随着信息技术的发展,图像因其信息量丰富的特点,成为通信和计算机系统中信息传输的重要载体,而图像信息占据了大量的存储容量,因而图像压缩编码是图像存贮的一个重要分支。本文首先介绍了图像压缩编码的研究背景,然后详细地从理论上介绍了利用小波变换来实现图像的压缩,通过Haar小波变换,Symlet小波变换,Coiflet小波变换以及db小波变换的理论研究及Matlab仿真分析,证明了Haar小波变换在图像压缩中的可行性。     

一种基于离散小波变换的图像数字水印算法

提出了一种以离散小波变换为基础的图像数字水印算法。详细介绍了离散小波变换和基于离散小波变换的数字水印嵌入算法及检测算法。     

小波变换的FPGA实现

为了实时进行不同小波基的快速小波变换,本文介绍了利用现场可编程阵列FPGA实现小波变换的设 计.     

基于提升小波变换的图像融合规则综述

对提升小波变换的基本原理进行了介绍,描述了基于提升小波变换的图像融合的主要步骤,对基于提升小波变换的图像融合规则进行了概括。     

小波图像编码与JPEG图像编码的比较研究

研究了JPEG和小波变换在图像压缩方面性能上的不同。介绍了JPEG图像编码方法的原理、小波变换图像编码方法 ,着重阐述了Mallat算法及其多分辨率分析方法。最后 ,对比了JPEG和小波变换图像编码 ,得出了JPEG和小波变换图像编码各自的优缺点。     

正交样条小波在图像压缩中的应用

给出了正交样条小波滤波器系数的计算方法和数据，将正交样条小波应用于图像压缩中，并与其他常用的小波如Daubechies小波和双正交小波进行了比较。结果表明，用正交样条小波进行图像压缩可以取得很好的效果。     

采用二维增强的三维小波视频编码

提出了一种采用二维增强的三维小波视频编码方法，该方法将序列图像信号作为三维信号，把视频图像的帧内相关性和帧间相关性同时组织在一起构建小波系数。同时利用二维小波进一步刻画三维小波变换后低频子带内的信息特点，与单纯三雏小波变换相比，本文提出的方法在相同码率时具有较高峰值信噪比，特别在高压缩比情况下重建图像具有更好的视觉效果。     

Four-Point Wavelets and Their Applications

Multiresolution analysis(MRA)and wavelets provide useful and efficient tools for representing functions at multiple levels of details.Wavelet representations have been used in a broad range of applications ,including image compression,physical simulation and numerical analysis,In this paper,the authors construct a new class of wavelets,called four-point wavelets,based on an interpolatory four-point subdvision scheme.They are of local support,symmetric and stable.The analysis and synthesis algorithms have linear time complexity,Depending on different weight parameters w.the scaling functions and wavelets generated by the four-point subdivision scheme are of different degrees of smoothness.Therefore th user can select better wavelets relevant to the practice among the classes of wavelets.The authors apply the four-point wavelets in signal compression.The results show that the four-point wavelets behave much better than B-spline wavelets in many situations.     

关于数字图像压缩中小波基选择问题的探讨

针对数字图像压缩编码中最优小波基的选择问题,论证了双正交样条小波基的优点,并对其进行了推导.样条小波的导数连续性保证了小波基的光滑性,双正交对偶小波的对称性使得滤波器具有线性相位,可减小失真,保证重构图像的质量.     

几种复小波在奇异性检测中效果的比较分析

介绍了信号奇异性检测的基本方法以及奇异性检测与小波变换的关系,基于复小波变换模极大方法检测奇异性的理论,在加性高斯白噪声环境下,分别用几种复小波检测了信号奇异点的位置,估计了信号奇异点的Lipschitz指数,并对实验结果进行了比较分析。     

Supercompact multiwavelets for flow field simulation

A supercompact multiwavelet scheme for computational fluid dynamics is presented. Beam and Warming's supercompact wavelet method is an appropriate wavelet for fluid simulation data in the sense that it can provide compact support. The compactness of the wavelets avoids unnecessary interaction with remotely located data (e.g. across a shock discontinuity or vortex) and significantly reduces computational data processing time. Thresholding for data compression with the supercompact wavelets is applied based on a covariance vector structure of multiwavelets. The extension of this scheme to three dimensions is analyzed. Numerical tests demonstrate that the analytic advantages actually result in large data compression ratios.     

二通道线性相位Neville-Lagrange提升小波滤波器组设计

基于提升格式的第二代小波可以通过对第一代小波滤波器组采用劳伦多项式的欧几里德分解而得到,而直接设计符合提升格式的二代小波一直是需要深入研究的热点问题.文中把Neville滤波器理论和Lagrange插值理论结合起来,构造了二通道线性相位Neville-Lagrange提升小波滤波器组,并证明了其线性相位性质,讨论了其归一化方法.文中给出了二通道线性相位的Neville-Lagrange-44(简称N-L-44)提升小波滤波器组实例,并与JPEG2000的9/7小波做了图像压缩实验比较.实验结果表明:N-L-44提升小波滤波器组的图像压缩效果要明显好于9/7小波滤波器组,其在低比特率(bpp<1)时的图像压缩效果要好于9/7小波的lifting格式.而且相对于9/7小波,二通道线性相位Neville-Lagrange提升小波滤波器组还具有良好的潜在发展空间,例如其可以用来构建自适应提升小波滤波器组,可以扩展到纯二维提升小波滤波器组等等.     

三维网格图形多分辨率分析与压缩

多分辨率分析和细分小波是近年来三维网格图形处理的新方法;该文实现了三维网格图形的网格细分连续重组和多分辨率分析算法,研究了基于细分小波系数选择的三维网格图形压缩。研究结果表明,对具有丰富冗余细节的三维网格图形,细分小波算法可以取得较好的压缩效果,该文还改进了Ｅｃｋ等提出的网格重组分区算法,使之更适用于一般的三维网格图形。     

Wavelet Compression and the Automatic Classification of Urban Environments Using High Resolution Multispectral Imagery and Laser Scanning Data

The field of wavelets has opened up new opportunities for the compression of satellite data. This paper examines the influence of data compression on the automatic classification of urban environments. Data from Daedalus airborne scanner imagery is used. Laser scanning altitude data is introduced as an additional channel alongside the spectral channels thus effectively integrating the local height and multispectral information sources. In order to incorporate context information, the feature base is expanded to include both spectral and non-spectral features. A maximum likelihood classification is then applied. It is demonstrated that the classification of urban scenes is considerably improved by fusing multispectral and geometric data sets. The fused imagery is then systematically compressed (channel by channel) at compression rates ranging from 5 to 100 using a wavelet-based compression algorithm. The compressed imagery is then classified using the approach described hereabove. Analysis of the results obtained indicates that a compression rate of up to 20 can conveniently be employed without adversely affecting the segmentation results.     

Design and Processing of Invertible Orientation Scores of 3D Images

The enhancement and detection of elongated structures in noisy image data are relevant for many biomedical imaging applications. To handle complex crossing structures in 2D images, 2D orientation scores \(U: {\mathbb {R}} ^ 2\times S ^ 1 \rightarrow {\mathbb {C}}\) were introduced, which already showed their use in a variety of applications. Here we extend this work to 3D orientation scores \(U: {\mathbb {R}} ^ 3 \times S ^ 2\rightarrow {\mathbb {C}}\). First, we construct the orientation score from a given dataset, which is achieved by an invertible coherent state type of transform. For this transformation we introduce 3D versions of the 2D cake wavelets, which are complex wavelets that can simultaneously detect oriented structures and oriented edges. Here we introduce two types of cake wavelets: the first uses a discrete Fourier transform, and the second is designed in the 3D generalized Zernike basis, allowing us to calculate analytical expressions for the spatial filters. Second, we propose a nonlinear diffusion flow on the 3D roto-translation group: crossing-preserving coherence-enhancing diffusion via orientation scores (CEDOS). Finally, we show two applications of the orientation score transformation. In the first application we apply our CEDOS algorithm to real medical image data. In the second one we develop a new tubularity measure using 3D orientation scores and apply the tubularity measure to both artificial and real medical data.