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Lastly, we present some theories of wavelet-based analysis of fractal image compression in chapter five. The more details of wavelet transform、wavelet frame、 wavelet basis、scaling function、reconstruction algorithm、decomposition algorithm and inverse formula are also discussed.

最后,我们在第五章介绍了基于小波分析的分形图象压缩的一些理论,还详细地讨论了小波变换、小波标架、小波基、尺度函数、重构算法、分解算法和反演公式。

The foundations theory of wavelet analysis are introduced, including integral wavelet transform , discrete wavelet transform , wavelet frames theory and its decomposition and reconstruction, multiresolution analysis theory and direct sum decomposition of L〓 space and reconstruction of functions based on multiresolution analysis theory.

介绍了小波分析理论的核心内容,包括积分小波变换、离散小波变换、小波框架理论以及小波框架的分解与重构、多分辨分析理论以及基于MRAT的L〓空间的分解与函数重构算法。

The principles of suppressing random noises with K-L transformation in wavelet conversion domain are that 1 wavelet decomposition is carried out on seismic signals to form wavelet packet sections in time sharing and frequency division, 2 K-L transformation is utilized to remove noises on sections, and 3 the de-noise wavelet packet sections are reconstituted into seismic sections to remove random noises.

介绍了小波变换域K-L变换压制随机噪声的基本原理,即先将地震信号进行小波分解形成分时分频的小波包剖面,然后用K-L,变换对小波包剖面进行去噪,再将去噪后的小波包剖面重构回地震剖面,从而达到消除随机噪声的目的。

Double Density Dual-Tree Complex Wavelet Transform integrates the advantages of double density wavelet, dual tree wavelet and complex wavelet. It has translation invariability and improved directionality. When it is introduced to image fusion, the characteristics of original images are extracted better and more information for fusion is obtained.

摘要双密度双树复数小波变换综合了双密度小波、双树小波和复数小波的优点,具有平移不变性以及良好的方向性,将其引入图像融合能够更好地提取原始图像的特征,为融合图像提供更多的信息。

At present, most of the image watermarking algorithms based on the wavelet transform fail to take into account the shortcoming that the first generation wavelet transform used in image processing will introduce quantization errors inevitably, because of the storing characteristics of the image. Wavelet transform that maps integers to integers will not introduce quantization errors. Its time-frequency analysis method and multi-scale property accordant with human being vision system makes integer wavelet transform an ideal way for digital watermarking.

目前,大多数基于小波变换的图像水印算法没有考虑到第一代小波变换用于图像处理中不可避免的引入量化误差的缺点,而整数小波变换除了具有小波的多分辨率分析与人类视觉特性一致、具有良好的时频特性等优点以外,还避免了第一代小波变换用于图像处理中引入量化误差等缺点。

At this text I bring forward effective project strategy of non-maturity haleness watermark model arithmetic. Making use of time-frequency local characteristic of wavelet switch, I bring forward digital image watermark insetting project basing on block of wavelet switch, at the first ,make the image disporting to block of 8×8,then make use of the characteristic of Haar wavelet switch,then make the image the second layer wavelet switch and carry through power modulus transaction.

本文提出了非完备性鲁棒性数字水印典型算法中的行之有效的设计策略,利用小波变换良好的时频局部特性,提出了基于块的小波变换的数字图像水印嵌入方案,把宿主图像分为8×8的小块,利用 Haar小波变换的特性,对图像进行二层小波变换分解,对变换系数进行权重处理,然后把每一个水印象素隐藏在相应的图像块的中低频小波系数之中,提高了数字水印的隐蔽性和鲁棒性。

The definition of Wavelet Analysis is that shifting the mother wavelet e.g. which has limited energy, such as shifting for, then proceeding dimensions, we obtained wavelet basis function ,, which make the inside product to the function to analysis With the Fourier transformation to the and, then the equivalent frequency spectrum of wavelet transformation can be expressed as where 、 are the transformations of 、 respectively and i is an imaginary number unit.

小波变换的含义是:把一具有有限能量的母小波,如进行移位后,再进行尺度的伸缩得到小波基函数为然后与待分析的函数作内积,即对和作Fourier变换后,可得到小波变换的等效频域表示为:其中、分别是、的Fourier变换,i为虚数单位。

This paper describes a wavelet filter using wavelet transform method,it obtains the rational formula of wavelet function around the mathematical approximation of a mother wavelet. By using Mexican Hat wavlet as an example to simulate the approximation process and using Matlab to simulate.

本文描述了一种用小波滤波器实现小波变换的方法,它通过对母小波的一种数值逼近得到小波函数的有理公式,并以Mexican Hat小波为例来模拟这个逼近过程并用Matlab对逼近过程进行仿真。

The choice of the best wavelet bases is one of the subjects attracting more attentions. This paper presents a new choosing method based on numerical analysis. Here the coding performance of wavelet bases is evaluated overall numerically by using several standards, which had been confirmed to be relating to image coding The best chosen wavelet bases fitting static images and video coding are respectively Daubechies's biorthogonal wavelet 9-7 and 5-3, which have been proved by coding experiments.

最佳小波基的选择是倍受关注的问题之一,本文提出一种新的基于数值分析的挑选方法,通过用几个已被证实是与图像编码密切相关的小波基评价标准对小波基的编码性能进行全面的数值评价,并经实际编码检验,选出了适宜静态与活动图像编码的最佳基分别为Daubechies双正交小波9-7与5-3。

The practical employment of multidimensional wavelet is only limited to tensor product wavelet. To construct a tensor product orthonormal wavelet basis in L〓, 2〓-1 different mother wavelets are used, and thus storing and computing wavelet basis of large dimension are of prohibitive cost.

根据Meyer的小波基存在性定理,利用张量积方法构造L〓的一个规范正交小波基,需要2〓-1个不同的函数,存储和计算方面的开销太大,在实时应用方面尚有很大的局限性。

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生产提出过百老汇的新的纽约市,在那里她赢得了约瑟夫calloway奖,她的表现,并于异型在美国的战区杂志之一, 10战区的青年艺术家观赏。

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