Graph Signal Restoration Using Nested Deep Algorithm Unrolling

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