Graph signal denoising using nested-structured deep algorithm unrolling

In this paper, we propose a deep algorithm unrolling (DAU) based on a variant of the alternating direction method of multiplier (ADMM) called Plug-and-Play ADMM (PnP-ADMM) for denoising of signals on graphs. DAU is a trainable deep architecture realized by unrolling iterations of an existing optimization algorithm which contains trainable parameters at each layer. We also propose a nested-structured DAU: Its submodules in the unrolled iterations are also designed by DAU. Several experiments for graph signal denoising are performed on synthetic signals on a community graph and U.S. temperature data to validate the proposed approach. Our proposed method outperforms alternative optimization- and deep learning-based approaches.