Compressive Recovery of Signals Defined on Perturbed Graphs
Abstract: Recovery of signals with elements defined on the nodes of a graph, from compressive measurements is an important problem, which can arise in various domains such as sensor networks, image reconstruction and group testing. In some scenarios, the graph may not be accurately known, and there may exist a few edge additions or deletions relative to a ground truth graph. Such perturbations, even if small in number, significantly affect the Graph Fourier Transform (GFT). This impedes recovery of signals which may have sparse representations in the GFT bases of the ground truth graph. We present an algorithm which simultaneously recovers the signal from the compressive measurements and also corrects the graph perturbations. We analyze some important theoretical properties of the algorithm. Our approach to correction for graph perturbations is based on model selection techniques such as cross-validation in compressed sensing. We validate our algorithm on signals which have a sparse representation in the GFT bases of many commonly used graphs in the network science literature. An application to compressive image reconstruction is also presented, where graph perturbations are modeled as undesirable graph edges linking pixels with significant intensity difference. In all experiments, our algorithm clearly outperforms baseline techniques which either ignore the perturbations or use first order approximations to the perturbations in the GFT bases.
Submission Length: Long submission (more than 12 pages of main content)
Previous TMLR Submission Url: https://openreview.net/forum?id=T3ejyiH6ns
Changes Since Last Submission: There was a font issue in the previous submission. We had used the TMLR style file, but we mistakenly had a line in our own latex code which invoked a different font. We have now fixed that issue, and double checked with some other submissions under review.
Assigned Action Editor: ~Stephen_Becker1
Submission Number: 3631
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