Compressive Sensing over Graphs [article]

Weiyu Xu, Enrique Mallada, Ao Tang
2010 arXiv   pre-print
In this paper, motivated by network inference and tomography applications, we study the problem of compressive sensing for sparse signal vectors over graphs. In particular, we are interested in recovering sparse vectors representing the properties of the edges from a graph. Unlike existing compressive sensing results, the collective additive measurements we are allowed to take must follow connected paths over the underlying graph. For a sufficiently connected graph with n nodes, it is shown
more » ... , using O(k (n)) path measurements, we are able to recover any k-sparse link vector (with no more than k nonzero elements), even though the measurements have to follow the graph path constraints. We further show that the computationally efficient ℓ_1 minimization can provide theoretical guarantees for inferring such k-sparse vectors with O(k (n)) path measurements from the graph.
arXiv:1008.0919v1 fatcat:ilz4ognowzb7neabiduqwzox3a