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首页> 外文期刊>IEEE Transactions on Information Theory >Fast algorithms for discrete and continuous wavelet transforms
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Fast algorithms for discrete and continuous wavelet transforms

机译：离散和连续小波变换的快速算法

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Several algorithms are reviewed for computing various types of wavelet transforms: the Mallat algorithm (1989), the 'a trous' algorithm, and their generalizations by Shensa. The goal of this work is to develop guidelines for implementing discrete and continuous wavelet transforms efficiently, and to compare the various algorithms obtained and give an idea of possible gains by providing operation counts. Most wavelet transform algorithms compute sampled coefficients of the continuous wavelet transform using the filter bank structure of the discrete wavelet transform. Although this general method is already efficient, it is shown that noticeable computational savings can be obtained by applying known fast convolution techniques, such as the FFT (fast Fourier transform), in a suitable manner. The modified algorithms are termed 'fast' because of their ability to reduce the computational complexity per computed coefficient from L to log L (within a small constant factor) for large filter lengths L. For short filters, smaller gains are obtained: 'fast running FIR (finite impulse response) filtering' techniques allow one to achieve typically 30% savings in computations.
机译：综述了几种用于计算各种类型的小波变换的算法：Mallat算法（1989年），“ trous”算法及其由Shensa进行的概括。这项工作的目的是制定有效实施离散和连续小波变换的准则，并比较所获得的各种算法，并通过提供运算次数给出可能的收益的想法。大多数小波变换算法都使用离散小波变换的滤波器组结构来计算连续小波变换的采样系数。尽管这种通用方法已经很有效，但是显示出可以通过以适当的方式应用已知的快速卷积技术（例如FFT（快速傅立叶变换））来获得可观的计算节省。修改后的算法之所以被称为“快速”，是因为它们能够将大滤波器长度L的每个计算系数的计算复杂度从L降低到log L（在较小的常数因子内）。对于短滤波器，可获得较小的增益：“快速运行” FIR（有限脉冲响应）滤波技术使一种方法通常可以节省30％的计算量。

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