In forward algorithm , we according to the high level coefficients to locate the jumps and modify the coarser level coefficients , which relate with the jumps . in inverse transforms algorithm , according to the locations to modify the datum , which relate with the jumps . we can reconstruct the image well by using this algorithm , and avoid the gibbs " phenomenon completely 该算法不必修改双正交小波变换及其滤波器系数，在小波图像分解时只是根据高频小波系数定位图像的跳跃处，修改关联跳跃处的粗尺度小波系数；重构时根据算法修改关联跳跃处的重构数据，就能很好地重构原图像，并从本质上消除了gibbs ’现象。
Fast algorithms of both discrete and orthonormal wavelet and wavelet packet coefficient are diagrammatized to be introduced . daubechies wavelet is applied to help to discuss the application and test on signal filtering and noise reduction with the principle and threshold implementation ; the basic principle to pickup the fault characteristics is introduced mainly about the relations between the maximum module and signal saltation point and how to characterize the saltation point with lipschitz exponent 展示了离散正交小波变换的mallat快速算法和小波包系数分解的快速算法；重点应用daubeches小波探讨了小波变换在信号滤波去噪中的应用和实验，阐述了其基本原理和通过阈值化处理实现滤波的具体方法；探讨了用小波变换进行故障特征提取的原理，说明了小波变换模极大值和信号突变点之间的关系以及怎样用李氏指数来表征突变点的性质。
Based on the decomposition of function space , mallat established the theory of multi - resolution when he research the image processing , which we can obtain the useful information through the characteristic of multi - scale of quadrature wavelet . the thoery of multi - resolution contacts the wavelet transform with the engineering application , which gives not only simple way of the structure of quadrature wavelet but also the academic basis of fast arithmetic on wavelet transform Mallat在研究图像处理时，从函数空间的分解出发，用正交小波基的多尺度特性将图像展开，获得有用信息进行处理，从而建立多分辨率分析理论。多分辨率分析不仅为正交小波基的构造提供了一种简单的方法，而且为正交小波变换的快速算法提供了理论依据，将小波变换与工程实践联系起来。
2 - d orthogonal wavelet transform and redundant wavelet transform are realized by use of mallat algorithm and trous algorithm respectively . then typical existent fusion algorithms based on orthogonal and redundant wavelet transform are summarized . standard deviation , entropy and average grads are advised to be the objective evaluation parameters 然后总结了现有典型的基于正交小波变换的像素级融合算法和基于冗余小波变换的图象融合算法，使用了标准差、信息熵和平均梯度三个标准作为融合结果的客观评价参数，并从理论上分析了各种算法的优劣。
In this paper , theories about wavelet analysis and image fusion are reviewed and remote - sensing image fusion is realized using wavelet analysis and unsupervised classification . first , wavelet transform theories are systematically reviewed and summarized from the point of view of signal and information processing 本文首先从小波理论在信号与信息处理学科领域中的应用角度对小波理论进行了系统的总结和介绍，分别利用mallat算法和trous算法实现了图象的正交小波变换和冗余小波变换。
The radar targets identification based on feature extraction with wavelet transformation and nearest - distance classer is studied in chapter 3 . discrete orthogonal wavelet transformation and wavelet transformation based on beylkin algorithm are applied to the samples of the targets to test their performance . the former has a better antinoise performance and the latter has a better identification rate 离散正交小波变换中提取的特征为信号的低频部分,在特征提取过程中已实现了消噪,具有较好的抗噪性能;而beylkin算法利用样本序列所有圆周移位的小波变换的高频部分,提取的信号特征虽具有移不变性,有较好的识别率,但抗噪性能较前者差。
To solve this inconsistency effectively , we don ’ t confine to one single fusion method or wavelet coefficients fusion rule , but combine them together and improve them . we consider several eigenvectors of the input images synthetically , and use the discrete biorthogonal wavelet transform at the lowest decomposition level to fulfill the new cwt - ihs multisensor remote sensing image fusion algorithm based on color compensation rule 为了有效地解决这一矛盾,本文不局限于单一的图像融合方法和小波系数融合规则,而是将各种方法和规则结合起来并加以改进,综合考虑输入图像的多个特征向量,用最低层的离散双正交小波变换实现了一种新的基于颜色补偿的cwt - ihs多源卫星遥感图像融合算法。
A new remote sensing image coding scheme based on the biorthogonal wavelet transform and revised spiht algorithm is proposed according to the statistical characteristic of remote sensing image data . the experimental results show that the proposed scheme could largely speed up the encoding process and reduce computational complexity on condition that reconstructed image quality is sacrificed little . meanwhile , this scheme has advantage over other algorithms in real time encoding 本文针对遥感图像的数据特点，提出了结合双正交小波变换和改进spiht算法的内嵌小波编码方案.实验结果表明，本文的方法能够在几乎不降低恢复图像质量的前提下降低了计算复杂度，提高了编码速度，有利于实时编码
