We consider the problem of designing spectral graph filters for the construction of dictionaries of atoms that can be used to efficiently represent signals residing on weighted graphs. While the filters used in previous spectral graph wavelet constructions are only adapted to the length of the spectrum, the filters proposed in this paper are adapted to the distribution of graph Laplacian eigenvalues, and therefore lead to atoms with better discriminatory power. Our approach is to first characterize a family of systems of uniformly translated kernels in the graph spectral domain that give rise to tight frames of atoms generated via generalized translation on the graph. We then warp the uniform translates with a function that approximates the cumulative spectral density function of the graph Laplacian eigenvalues. We use this approach to construct computationally efficient, spectrum-adapted, tight vertexfrequency and graph wavelet frames. We give numerous examples of the resulting spectrum-adapted graph filters, and also present an illustrative example of vertex-frequency analysis using the proposed construction. Index Terms-Filter design, signal processing on graphs, spectrum-based warping, tight frames, vertex-frequency analysis.
A spectrum-adapted tight vertex-frequency frame is proposed in REF via translation on the graph.
Spectrum-Adapted Tight Graph Wavelet and Vertex-Frequency Frames
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Mathematics Computer Science