Design of Orthogonal Graph Wavelet Filter Banks

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 lambda = 0 and lambda = 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.