Joint Data Inpainting and Graph Learning via Unrolled Neural Networks

Given partial measurements of a time-varying graph signal, we propose an algorithm to simultaneously estimate both the underlying graph topology and the missing measurements. The proposed algorithm operates by training an interpretable neural network, designed from the unrolling framework. The proposed technique can be used both as a graph learning and a graph signal reconstruction algorithm. This work enhances prior work in graph signal reconstruction by allowing the underlying graph to be unknown; and also builds on prior work in graph learning by tailoring the learned graph to the signal reconstruction task.