二维四通道不可分正交小波的快速算法

刘斌; 秦志敏

doi:doi:10.3969/j.issn.1007-5461. 2017.05.004

量子电子学报, 2017, 34 (5): 530, 网络出版: 2017-10-30

二维四通道不可分正交小波的快速算法

Fast algorithm for two-dimensional four-channel non-separable orthogonal wavelet

论文大纲

刘斌 ^*秦志敏

作者单位

湖北大学计算机与信息工程学院, 湖北武汉 430062

图像处理不可分小波二维四通道 Mallat算法滤波器组 image processing non-separable wavelet two-dimensional four-channel Mallat algorithm filter banks

摘要

针对张量积小波只强调水平、垂直方向的不足,研究了二维小波的性质和特点,给出了二维四通道不可分小波的快速算法及其数学证明,分析了此算法的运算量,探讨了滤波器组的构造方法,理论推导与分析表明此算法运算速度比不抽样的二维不可分小波变换和二维快速Fourier变换更快。通过构造出的滤波器组进行不可分小波的分解实验,并与张量积小波进行比较,结果表明不可分小波变换在对图像进行滤波时能全面提取图像各方向的信息。

Abstract

Aiming at the shortage that tensor product wavelet only emphasizes the horizontal and vertical directions, the properties and characteristics of two-dimensional wavelet are investigated. A fast algorithm for two-dimensional four-channel non-separable wavelet and its mathematical proof are presented. The computation of the algorithm is analyzed, and the construction method of filter banks is discussed. Theoretical deduction and analysis show that the computation speed of this algorithm is faster than that of the non-sampling two-dimensional non-separable wavelet transform and two-dimensional fast Fourier transform. The decomposition experiment of non-separable wavelet is performed by constructing filter banks, and it’s compared with the tensor product wavelet. Results show that the non-separable wavelet transform can extract more comprehensive information of each direction when the image is filtered.

参考文献

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刘斌, 秦志敏. 二维四通道不可分正交小波的快速算法[J]. 量子电子学报, 2017, 34(5): 530. LIU Bin, QIN Zhimin. Fast algorithm for two-dimensional four-channel non-separable orthogonal wavelet[J]. Chinese Journal of Quantum Electronics, 2017, 34(5): 530.

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