Generalized Sampling on Graphs with A Subspace Prior

We consider a framework for generalized sampling of graph signals that extends sampling results in shift-invariant (SI) spaces to the graph setting. We assume that the input signal lies in a periodic graph spectrum subspace, which generalizes the standard SI assumption to graph signals. Sampling is performed in the graph frequency domain by an arbitrary graph filter. We show that under a mild condition on the sampling filter, perfect recovery is possible using a correction filter that can be represented as a spectral graph filter whose response depends on the prior subspace spectrum and on the sampling filter. This filter parallels the correction filter in SI sampling in standard signal processing. Since the input space and the sampling filter are almost arbitrary, our framework allows perfect recovery of many classes of input signals from a variety of different sampling patterns using a simple correction filter. For example, our method enables perfect recovery of non-bandlimited graph signals from their bandlimited measurements.