Local two-channel critically sampled filter-banks on graphs

In this paper, we propose two-channel filter-bank designs for signals defined on arbitrary graphs. These filter-banks are local, invertible and critically sampled. Depending on the chosen downsampling method, we obtain two design techniques. We propose general 2-channel transforms, where output signal is downsampled to guarantee invertibility. We also propose a lifting-based approach, where signals are downsampled before applying the transforms. Our proposed transforms are polynomials of the graph Laplacian matrix and have a simple spectral interpretation.