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. Graph signals are often corrupted through sensing
processes, and need to be restored for the above applications. 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
propose a general restoration method for linear degradation by unrolling
iterations of Plug-and-Play ADMM (PnP-ADMM). In the second method, the unrolled
ADMM-based denoiser is incorporated as a submodule. Therefore, our restoration
method has a nested DAU structure. Thanks to DAU, parameters in the proposed
denoising/restoration methods are trainable in an end-to-end manner. Since the
proposed restoration methods are based on iterations of a (convex) optimization
algorithm, the method is interpretable and keeps the number of parameters small
because we only need to tune graph-independent regularization parameters. We
solve two main problems 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 to several
existing methods in terms of root mean squared error in both tasks