Joint Data Inpainting and Graph Learning via Unrolled Neural Networks
Subbareddy Batreddy, Pushkal Mishra, Yaswanth Kakarla, Aditya Siripuram
TL;DR
This work tackles the challenge of recovering missing entries and learning an unknown graph topology from time-varying graph signals. It introduces an unrolled, interpretable neural network that interleaves data-inpainting with graph learning through an alternating minimization framework, leveraging a higher-order temporal smoothness prior $\mathpzc{V}_{\mathcal{G}}(\mathbf{X},\bar{\alpha})$ and a learnable $Z(\bar{\alpha})$. The model optimizes a joint objective that blends data fidelity, graph variation, and Laplacian regularization, and trains by unrolling iterations into network layers, with $\bar{\alpha}$ learned end-to-end. Empirical results on real (Brittany temperature, Open Neuro fMRI) and synthetic data demonstrate improved reconstruction accuracy and more faithful graph recovery than baselines, even at low sensing ratios and in the presence of noise. The approach streamlines dual tasks—data inpainting and graph learning—enabling applications in GSP tasks beyond inpainting and offering a framework for tailoring graphs to the specific reconstruction objective.
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.