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.

1. Introduction

Many sensing devices capture and store various signals. Since observed signals via such devices frequently suffer from noise or missing values as a consequence of the sensing process, signal restoration methods have been intensively studied in signal processing. The goal of signal restoration is to recover the original signal from observation(s) by solving an inverse problem which includes blind deconvolution [1], denoising [2], and interpolation [3].