Sparse signals on hypergraphs

Abstract

AbstractSignals with a sparse representation in a given basis as well as Laplacian eigenvectors of graphs play a big role in signal processing and machine learning. We put these topics together and look at signals on graphs that have a sparse representation in the basis of eigenvectors of the Laplacian matrix, which may appear after convolution with an unknown sparse filter. We give explicit algorithms to recover those sums by sampling the signal only on few vertices, i.e., the number of required samples is independent of the total size of the graph and takes only local properties of the graph into account. We generalize these methods to simplicial complexes.