The Network Nullspace Property for Compressed Sensing of Big Data over Networks
This work addresses efficient compressed sensing for big data over networks, providing a theoretical foundation for designing sampling strategies based on network topology.
The paper tackles the problem of accurately recovering graph signals from massive network-structured datasets using few signal values by introducing the network nullspace property, which ensures recovery by coupling network cluster structure with sampling set geometry.
We present a novel condition, which we term the net- work nullspace property, which ensures accurate recovery of graph signals representing massive network-structured datasets from few signal values. The network nullspace property couples the cluster structure of the underlying network-structure with the geometry of the sampling set. Our results can be used to design efficient sampling strategies based on the network topology.