Design of orthogonal graph wavelet filter banks
Design of orthogonal graph wavelet filter banks
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DOI：
10.1109/iecon.2016.7793133
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发表时间：
2016-10
期刊：
影响因子：
--
通讯作者：
Xi Zhang
中科院分区：
文献类型：
--
作者：
Xi Zhang
提出了一种新的双通道紧支撑近正交图小波滤波器组的设计方法。首先证明了滤波器组正交的必要条件，即如果具有平坦阻带，则核滤波器在通带内必须具有平坦谱，然后推导出最大平坦滤波器的封闭解。我们还给出了一个滤波器函数，该滤波器函数确保了最大平坦滤波器在λ = 0和λ = 2处的指定平坦度。因此，我们可以利用剩余的系数来最小化滤波器组的重构误差，其中使用Matlab中的优化工具来设计滤波器组，而不需要任何初始解。用该方法设计了一些算例，并与传统的设计方法进行了比较。实验结果表明，本文提出的图滤波器组的性能优于传统的核滤波器。最后，提出的图小波应用到明尼苏达州的交通图，以证明所提出的设计方法的有效性。
This paper proposes a novel design method of two channel compactly supported near orthogonal graph wavelet filter banks. We firstly prove the necessary condition for the orthogonality of filter banks where the kernel filter must have a flat spectral in passband if having flat stopband, and then derive the closed-form solution for the maximally flat filters. We also give a filter function that ensures the specified degrees of flatness at λ = 0 and λ = 2 by the maximally flat filters. Therefore, we can use the remaining coefficients to minimize the reconstruction error of filter banks, where the optimization tool in Matlab is used to design the filter banks without any initial solution. Some examples are designed by using the proposed method and the spectral are compared with the conventional design methods. It is shown from the experimental results that the graph filter banks proposed in this paper outperform the conventional kernel filters. Finally, the proposed graph wavelets are applied to the Minnesota traffic graph to demonstrate the effectiveness of the proposed design method.