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2002年，MN Do和Martin Vetterli提出了一种“真正”的图像二维表示方法：Contourlet变换，也称塔型方向滤波器组(Pyramidal Directional Filter Bank, PDFB)。Contourlet变换是利用拉普拉斯塔形分解(LP)和方向滤波器组(DFB)实现的另一种多分辨的、局域的、方向的图像表示方法。(In 2002, MN Do and Martin Vetterli proposed a "real" two-dimensional representation of images: Contourlet transform, also known as Pyramidal Directional Filter Bank (PDFB). Contourlet transform is another multi-resolution, local and directional image representation method based on Laplacian pyramid decomposition (LP) and directional filter banks (DFB).)

说明：  直接减压到matlab\work目录下就可以看到运行结果了，其中包括了位平面分解，量化嵌入（提取），图像的金字塔分解等的程序块。(decompression directly to the Matlab \ work on the directory can see the results, which included a bit plane decomposition, quantification embedded (extraction), the image of the pyramid decomposition of the block.)

小波变换测试，小波分解的级数设置为3级，可以实现数字图像的小波变化和逆变化。测试代码请使用512*512灰度图像(The wavelet transformation test, wavelet decomposition series is set to 3, digital image wavelet changes and reverse changes.)

小波变换(wavelet transform，WT)是一种新的变换分析方法，它继承和发展了短时傅立叶变换局部化的思想，同时又克服了窗口大小不随频率变化等缺点，能够提供一个随频率改变的"时间-频率"窗口，是进行信号时频分析和处理的理想工具。它的主要特点是通过变换能够充分突出问题某些方面的特征，能对时间(空间)频率的局部化分析，通过伸缩平移运算对信号(函数)逐步进行多尺度细化，最终达到高频处时间细分，低频处频率细分，能自动适应时频信号分析的要求，从而可聚焦到信号的任意细节，解决了Fourier变换的困难问题，成为继Fourier变换以来在科学方法上的重大突破。(Wavelet transform (WT) is a new transform analysis method. It inherits and develops the idea of localization of short-time Fourier transform and overcomes the shortcomings that window size does not vary with frequency. It can provide a frequency-dependent The Time-Frequency window is ideal for time-frequency analysis and processing of signals. Its main feature is that by transforming some features that can fully highlight some aspects of the problem, the localization of the time (space) frequency can be analyzed, and the signal (function) can be gradually and multi-scale refined by the scaling operation, finally reaching the high frequency Time subdivision, frequency subdivision at low frequencies, can automatically adapt to the requirements of time-frequency signal analysis, which can focus on any details of the signal to solve the difficulties of Fourier transform has become a major breakthrough in the scientific method since Fourier transform.)

基于小波变换的图像压缩编码，实现了多种小波变换，并且实现了12:1的高压缩率。(Based on Wavelet Transform Image Coding, to achieve a variety of wavelet transform, and achieved a high 12:1 compression ratio.)

说明：  使用小波变换技术实现图像分割，利用matlab编程实现(Using wavelet transform technology to achieve image segmentation, matlab programming)

MATLAB实现小波变换经典程序，包括采用多孔trous算法实现小波变换、基于小波消噪的雷达回波检测、小波插值与小波构造、小波滤波器构造和消噪程序、小波谱分析mallat算法经典程序、小波图像重构 Matlab 程序等等(MATLAB wavelet transform classic program, including the use of undecimated wavelet transform algorithm to achieve the wavelet transform, the radar echo detection based on wavelet denoising, wavelet interpolation and wavelet construction, construction and de-noising of the wavelet filter program, a small spectral analysis mallatclassic algorithm procedures, wavelet image reconstruction Matlab programalgorithm)

实现离散余弦(TCD)变换(achieve discrete cosine (TCD) Transform)

利用小波提升算法实现了第二代小波变换,将之应用在信号去噪中,实现了数据的边界对称延拓,去噪效果较好.(Wavelet Lifting algorithm using the second generation wavelet transform, to be used in signal de-noising, the realization of the data symmetric boundary extension, denoising better.)

matlab实现的多相滤波器，cic抽取D=5时例子，及级联型的cic的程序。(matlab implementation of the polyphase filter, cic examples taken D = 5 时, and the cascade of cic procedures.)