Random sampling of bandlimited signals on graphs
This work addresses efficient signal sampling on graphs for applications in network data analysis, representing an incremental improvement with specific algorithmic advances.
The paper tackles the problem of sampling bandlimited signals on graphs by proposing two random sampling strategies, one non-adaptive and one adaptive, with the adaptive method requiring only O(k log(k)) measurements for accurate and stable recovery, and includes a computationally efficient decoder validated through experiments.
We study the problem of sampling k-bandlimited signals on graphs. We propose two sampling strategies that consist in selecting a small subset of nodes at random. The first strategy is non-adaptive, 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 k-bandlimited 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 k-bandlimited 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.