  Graph signal processing is a ubiquitous task in many applications such as
sensor, social, transportation and brain networks, point cloud processing, and
graph neural networks. Often, graph signals are corrupted in the sensing
process, thus requiring restoration. In this paper, we propose two graph signal
restoration methods based on deep algorithm unrolling (DAU). First, we present
a graph signal denoiser by unrolling iterations of the alternating direction
method of multiplier (ADMM). We then suggest a general restoration method for
linear degradation by unrolling iterations of Plug-and-Play ADMM (PnP-ADMM). In
the second approach, the unrolled ADMM-based denoiser is incorporated as a
submodule, leading to a nested DAU structure. The parameters in the proposed
denoising/restoration methods are trainable in an end-to-end manner. Our
approach is interpretable and keeps the number of parameters small since we
only tune graph-independent regularization parameters. We overcome two main
challenges in existing graph signal restoration methods: 1) limited performance
of convex optimization algorithms due to fixed parameters which are often
determined manually. 2) large number of parameters of graph neural networks
that result in difficulty of training. Several experiments for graph signal
denoising and interpolation are performed on synthetic and real-world data. The
proposed methods show performance improvements over several existing techniques
in terms of root mean squared error in both tasks.
