Random sampling of bandlimited signals on graphs
Abstract
We study the problem of sampling kbandlimited signals on graphs. We propose two sampling strategies that consist in selecting a small subset of nodes at random. The first strategy is nonadaptive, i.e., independent of the graph structure, and its performance depends on a parameter called the graph coherence. On the contrary, the second strategy is adaptive but yields optimal results. Indeed, no more than O(k log(k)) measurements are sufficient to ensure an accurate and stable recovery of all kbandlimited signals. This second strategy is based on a careful choice of the sampling distribution, which can be estimated quickly. Then, we propose a computationally efficient decoder to reconstruct kbandlimited signals from their samples. We prove that it yields accurate reconstructions and that it is also stable to noise. Finally, we conduct several experiments to test these techniques.
 Publication:

arXiv eprints
 Pub Date:
 November 2015
 DOI:
 10.48550/arXiv.1511.05118
 arXiv:
 arXiv:1511.05118
 Bibcode:
 2015arXiv151105118P
 Keywords:

 Computer Science  Social and Information Networks;
 Computer Science  Machine Learning;
 Statistics  Machine Learning