2022/08/04 by Junxia You, You, Junxia, Lihua Yang +1
Computer Science · Biochemistry, Genetics and Molecular Biology · #Advanced Graph Neural Networks #Receptor Mechanisms and Signaling
paper · pdf · doi:10.48550/arxiv.2208.02631
In this paper, we propose the construction of critically sampled perfect reconstruction two-channel filterbanks on arbitrary undirected graphs.Inspired by the design of graphQMF proposed in the literature, we propose a general ``spectral folding property'' similar to that of bipartite graphs and provide sufficient conditions for constructing perfect reconstruction filterbanks based on a general graph Fourier basis, which is not the eigenvectors of the Laplacian matrix. To obtain the desired graph Fourier basis, we need to solve a series of quadratic equality constrained quadratic optimization problems (QECQPs) which are known to be non-convex and difficult to solve. We develop an algorithm to obtain the global optimal solution within a pre-specified tolerance. Multi-resolution analysis on real-world data and synthetic data are performed to validate the effectiveness of the proposed filterbanks.