Two Channel Filter Banks on Arbitrary Graphs With Positive Semi Definite Variation Operators

We propose novel two-channel filter banks for signals on graphs. Our designs can be applied to arbitrary graphs, given a positive semi definite variation operator, while using vertex partitions downsampling. The proposed generalized (GFBs) also satisfy several desirable properties including perfect reconstruction and critical sampling, having efficient implementations. results generalize previous approaches that were only valid the normalized Laplacian of bipartite approach is based graph Fourier transforms (GFTs) by eigenvectors operator. These GFTs are orthogonal in an alternative inner product space which depends downsampling operators. key theoretical contribution showing spectral folding property at core bank theory, GFT if matrix chosen properly. In addition, we study domain GFBs illustrate their probabilistic interpretation Gaussian graphical models. While defined any choice partition downsampling, algorithm optimize these with criterion favors balanced large cuts, shown lead stable GFB numerical experiments show partition-optimized implemented efficiently 3D point clouds hundreds thousands points (nodes), improving color signal representation quality over competing state-of-the-art approaches.