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This paper focuses on the construction of true bidimensional wavelets by lifting scheme and the relevant image coding. We research the nonseparable bidimensional interpolator designed by different standards, carry out the true bidimensional wavelet decomposition and improve the SPIHT coding in order to adapt to the characteristic of true bidimensional wavelet decomposition. It is proved by experiments that the subjective and objective quality of binary tree SPIHT on true bidimensional wavelet decomposition is better than famous 9/7 wavelet under the condition of low bits compression.

本文以基于提升格式的纯二维小波滤波器组的构造为中心,研究了不同类型的二维不可分离内插滤波器,实现了图像的纯二维小波分解,并改进了SPIHT编码算法,使其适合纯二维小波的分解特点,实验证明在低比特压缩下,纯二维小波分解的二叉树SPIHT在主观和客观质量上要好于著名的9/7小波。

Secondly, Pre-emphasis is used to improve the high boost in WWF algorithm. In the same way, using an effective frame regrouping precept improve frame overlapping and regrouping, designing an new SH window to window function's design, selecting coif wavelet as the analysis wavelet basis to wavelet basis's selection, discarding the unvoiced frames by threshold-wavelet transform to unvoiced/voiced frames' distinguish, and solving the wiener gain by the fake cepstral subtraction to Wiener gain's getting as well.

采用进行预加重处理、设计有效的帧重组方案、自定义SH窗、选用coif小波作为分析用小波基、采用加阈值小波变换法去除清音帧,和基于伪倒谱相减法求解维纳滤波增益系数等方法,分别对模型中高频提升、帧重叠与重组、窗函数设计、小波基选取、清浊音判别及维纳滤波增益系数获取等实现细节进行研究和改进。

Secondly, brief to introduce Wavelet Transform definition. Mallat algorithm, two-dimensional wavelet decomposability of image and orthogonal wavelet decomposability. And the zero tree structure of image wavelet transform.

其次,简要介绍了小波变换的定义、Mallat算法、图像的二维正交小波分解以及图像小波变换的零树结构。

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。

The uniform approximation of normal wavelet neural network and the robust analysis of wavelet neural networks of the combination of Sigmoid function are detailedly introduction; Multiple model failure detection based on wavelet neural network is demonstrated detailedly; At last, the failure diagnosis results of aerocraft is present seperately by employing wavelet neural network and BP neural network, and the fault diagnosis of areocraft system by wavelet neural network is achieved.

论文以小波神经网络为研究对象,提出了一类新的加权小波基,分析证明了加权小波基的诸多良好特性;对于常见小波神经网络的一致逼近特性、S型函数组合小波神经网络的鲁棒性分析、多模型小波神经网络的故障检测等问题给出了详细的论证;最后,针对歼击机的常见故障问题,分别给出了应用小波神经网络和BP神经网络的故障诊断结果,实现了小波神经网络对飞机系统的故障诊断。

At the second place, feasibility of edge detection based on orthogonal wavelet is discussed in the article. Its theoretical key of edge detection based on orthogonal wavelet that approximate symmetrical or antisymmetrical orthogonal real wavelet can be constructed though Haar wavelet is the only symmetrical or antisymmetrical orthogonal real wavelet.

随后本文讨论了正交小波基用于边缘检测的可行性:虽然除了Haar小波外再也找不到对称或反对称的正交实小波,但是可以构造出近似对称或反对称的正交实小波,这就是正交小波用于边缘检测的理论关键。

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