Design of Two Channel Biorthogonal Graph Wavelet Filter Banks with Half-Band Kernels

In this paper, we propose a novel design method of two channel critically sampled compactly supported biorthogonal graph wavelet filter banks with half-band kernels. First of all, we use the polynomial half-band kernels to construct a class of biorthogonal graph wavelet filter banks, which exactly satisfy the PR (perfect reconstruction) condition. We then present a design method of the polynomial half-band kernels with the specified degree of flatness. The proposed design method utilizes the PBP (Parametric Bernstein Polynomial), which ensures that the half-band kernels have the specified zeros at λ = 2. Therefore the constraints of flatness are satisfied at both of λ = 0 and λ = 2, and then the resulting graph wavelet filters have the flat spectral responses in passband and stopband. Furthermore, we apply the Remez exchange algorithm to minimize the spectral error of lowpass (highpass) filter in the band of interest by using the remaining degree of freedom. Finally, several examples are designed to demonstrate the effectiveness of the proposed design method. key words: graph signal processing, graph wavelets, biorthogonal graph filter bank, polynomial half-band kernel, Remez exchange algorithm, flatness