Sampling and Reconstruction of Diffused Sparse Graph Signals From Successive Local Aggregations

We analyze the sampling and posterior recovery of diffused sparse graph signals from observations gathered at a single node by using an aggregation sampling scheme. Diffused sparse graph signals can be modeled as the output of a linear graph filter to a sparse input and are useful in scenarios where a few seeding (source) nodes generate a non-zero input, which is then diffused according to the network dynamics dictated by the filter. Instead of considering a traditional setup where the observations correspond to the signal values at a subset of nodes, here the observations are obtained locally at a single node via the successive aggregation of its own value and that of its neighbors. Depending on the particular application, the goal is to use the local observations to recover the diffused signal or (the location and values of) the seeds. Different sampling configurations are investigated, including those of known and unknown locations of the sources as well as those of the diffusing filter being unknown.