Design of Near Orthogonal Graph Filter Banks

The processing of signal on graphs is becoming an important emerging area that has great potential in a wide variety of applications, e.g. social network. The work by Narang and Ortega (2012) laid the framework for critically sampled orthogonal two-channel filter bank for signal on undirected bipartite graphs. The design method presented by Narang and Ortega (2012) does not allow the tailoring of the filters spectral response and the control of the reconstruction error of the filter bank. This work present a method to design spectral filters that is based on Bernstein polynomial approximation and constrained optimization. The method allows the trade-off between transition band sharpness, ripple magnitude and reconstruction error.