Sub graph-based filter banks for graph signals - 2016
We design a critically-sampled compact-support biorthogonal remodel for graph signals, via graph filterbanks. Instead of partitioning the nodes in two sets therefore as to remove one each 2 nodes within the filterbank downsampling operations, the planning relies on a partition of the graph in connected subgraphs. Coarsening is achieved by defining one “supernode” for each subgraph and the perimeters for this coarsened graph derives from the connectivity between the subgraphs. Unlike the “one every 2 nodes” downsampling on bipartite graphs, this coarsening operation will not have an precise formulation within the graph Fourier domain. Instead, we rely on the local Fourier bases of each subgraph to outline filtering operations. We tend to apply successfully this methodology to decompose graph signals, and show promising performance on compression and denoising.
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