Joint Data Inpainting and Graph Learning via Unrolled Neural Networks

TL;DR

This paper introduces an unrolled neural network approach for joint graph topology estimation and signal inpainting from partial measurements, improving adaptability and accuracy in dynamic graph signal processing.

Contribution

It presents a novel interpretable neural network framework that simultaneously learns the graph structure and reconstructs missing signals, unifying graph learning and inpainting tasks.

Findings

Effective joint graph learning and signal reconstruction demonstrated.

Outperforms traditional methods in accuracy and adaptability.

Applicable to various time-varying graph signal scenarios.

Abstract

Given partial measurements of a time-varying graph signal, we propose an algorithm to simultaneously estimate both the underlying graph topology and the missing measurements. The proposed algorithm operates by training an interpretable neural network, designed from the unrolling framework. The proposed technique can be used both as a graph learning and a graph signal reconstruction algorithm. This work enhances prior work in graph signal reconstruction by allowing the underlying graph to be unknown; and also builds on prior work in graph learning by tailoring the learned graph to the signal reconstruction task.