A general approach for analysis and application of discrete multiwavelet transforms
A general approach for analysis and application of discrete multiwavelet transforms
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DOI：
10.1109/78.823972
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发表时间：
2000-02
期刊：
影响因子：
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通讯作者：
J. Y. Tham;Lixin Shen;Seng Luan Lee;Hwee Huat Tan
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文献类型：
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作者：
J. Y. Tham;Lixin Shen;Seng Luan Lee;Hwee Huat Tan
本文提出了一种分析和应用离散多小波变换的通用范例，特别是在图像压缩方面。首先，我们建立了等效标量（小波）滤波器组系统的概念，在这个概念中，我们用r个等效标量滤波器组的集合给出了重数r的多小波系统的等价和充分表示。这种关系激发了一种新的度量，称为良好多滤波器特性（gmp），它定义了等效标量滤波器的理想滤波器特性。然后，我们将gmp的概念直接与矩阵滤波器联系起来，作为给定多小波系统的细化掩模的必要特征向量属性。其次，我们通过设计适当的预分析和合成后多速率滤波技术，提出了一个通用的、高效的、无冗余的多小波初始化框架。最后，我们的仿真验证了具有gmp并采用所提出的初始化技术的正交和双正交多小波都比流行的标量小波（如Daubechies的d8小波和D（9/7）小波）性能更好，并且其中一些多小波以更低的计算复杂度实现了这一点。
This paper proposes a general paradigm for the analysis and application of discrete multiwavelet transforms, particularly to image compression. First, we establish the concept of an equivalent scalar (wavelet) filter bank system in which we present an equivalent and sufficient representation of a multiwavelet system of multiplicity r in terms of a set of r equivalent scalar filter banks. This relationship motivates a new measure called the good multifilter properties (GMPs), which define the desirable filter characteristics of the equivalent scalar filters. We then relate the notion of GMPs directly to the matrix filters as necessary eigenvector properties for the refinement masks of a given multiwavelet system. Second, we propose a generalized, efficient, and nonredundant framework for multiwavelet initialization by designing appropriate preanalysis and post-synthesis multirate filtering techniques. Finally, our simulations verified that both orthogonal and biorthogonal multiwavelets that possess GMPs and employ the proposed initialization technique can perform better than the popular scalar wavelets such as Daubechies'D8 wavelet and the D(9/7) wavelet, and some of these multiwavelets achieved this with lower computational complexity.