Graph signal recovery from incomplete and noisy information using approximate message passing

We consider the problem of recovering a graph signal from noisy and incomplete information. In particular, we propose an approximate message passing based iterative method for graph signal recovery. The recovery of the graph signal is based on noisy signal values at a small number of randomly selected nodes. Our approach exploits the smoothness of typical graph signals occurring in many applications, such as wireless sensor networks or social network analysis. The graph signals are smooth in the sense that neighboring nodes have similar signal values. Methodologically, our algorithm is a new instance of the denoising based approximate message passing framework introduced recently by Metzler et. al. We validate the performance of the proposed recovery method via numerical experiments. In certain scenarios our algorithm outperforms existing methods.