Techniques for constructing biorthogonal bipartite graph filter banks

The processing of data defined on irregular discrete domains, i.e., graph signals, is becoming an emerging area with great application potential. Using spectral graph theory, Narang and Ortega (2013) laid the framework for two channel filter banks with critical sampling for bipartite graph signals. The bipartite graph filter bank can be extended to any arbitrary graph using the notion of separable filtering. The design of the biorthogonal filter banks by Narang and Ortega (2013) is based on the factorization of a maximally flat polynomial. The factorization technique does not allow much control of the spectral response of the graph filters, resulting in response asymmetry. In this paper, we present a generic framework for constructing biorthogonal graph filter banks that does not require factorization. We introduce the notion of polyphase representation and ladder structures for graph filter banks. We show that filters having virtual spectral symmetry and almost energy preservation can be constructed without any sophisticated optimization. Fine control of the spectral response can also be achieved with ease.