Design of Nonsubsampled Graph Filter Banks via Lifting Schemes

© 1994-2012 IEEE. Graph filter banks play a crucial role in the vertex and spectral representation of graph signals. The notion of two-channel nonsubsampled graph filter banks (NSGFBs) on an undirected graph was introduced recently. The absence of downsampling/upsampling operators allows greater flexibility in the design of NSGFBs that achieve perfect reconstruction. However the design of NSGFBs that take the spectral response into account has not been adequately addressed yet. Based on the polynomial/rational lifting scheme, this letter presents a simple method to design NSGFBs with good spectral response and perfect reconstruction. Experimental results will demonstrate the effectiveness of the proposed method in tailoring the spectral responses of the lifted NSGFBs. Application of the NSGFB to denoising will also be considered.