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In this paper, we propose the construction of critically sampled perfectreconstruction two-channel filterbanks on arbitrary undirected graphs.Inspiredby the design of graphQMF proposed in the literature, we propose a general``spectral folding property'' similar to that of bipartite graphs and providesufficient conditions for constructing perfect reconstruction filterbanks basedon a general graph Fourier basis, which is not the eigenvectors of theLaplacian matrix. To obtain the desired graph Fourier basis, we need to solve aseries of quadratic equality constrained quadratic optimization problems(QECQPs) which are known to be non-convex and difficult to solve. We develop analgorithm to obtain the global optimal solution within a pre-specifiedtolerance. Multi-resolution analysis on real-world data and synthetic data areperformed to validate the effectiveness of the proposed filterbanks.

Perfect Reconstruction Two-Channel Filter Banks on Arbitrary Graphs Based on an Optimization Model