Algorithm Unrolling-based Denoising of Multimodal Graph Signals

TL;DR

The paper addresses denoising multimodal signals on graphs when spatial and modality graphs are unknown. It introduces a twofold-graph denoising framework that alternates between signal smoothing and joint graph learning, with a closed-form update for the signal and a primal-dual splitting (PDS) solver for the graph-learners, all wired into a deep algorithm unrolling (DAU) architecture to learn layer-wise parameters. The main contributions are the simultaneous estimation of two graphs during denoising, a PDS-based solver for the graph-learning subproblems, and a DAU scheme that reduces manual tuning while enabling end-to-end training; experiments on synthetic and real data show superior performance over model-based, GCN-based, and DAU-based baselines. This approach is particularly impactful for sensor networks and multimodal data where graph structure is not available a priori, enabling robust, interpretable denoising with learned relational structure.

Abstract

We propose a denoising method for multimodal graph signals by an alternating minimization scheme that sequentially solves signal restoration and graph learning problems. Many complex-structured data, i.e., those on sensor networks, can capture multiple modalities at each measurement point, referred to as modalities. They are also assumed to have an underlying structure or correlations in modality as well as space. Such multimodal data are regarded as graph signals on a twofold graph and they are often corrupted by noise. Furthermore, their spatial/modality relationships are not always given a priori: We need to estimate twofold graphs during a denoising algorithm. In this paper, we consider a signal denoising method on twofold graphs, where graphs are learned simultaneously. Specifically, the graph learning subproblems are solved using the primal-dual splitting (PDS) algorithm, while the signal update has a closed-form solution. Parameters in this iterative algorithm are learned from training data by unrolling the iteration with deep algorithm unrolling. Experimental results on synthetic and real-world data demonstrate that the proposed method outperforms existing model- and deep learning-based graph signal denoising methods.

Figures (61)

• Figure 1: A multimodal graph signal on a twofold graph.
• Figure 2: Overview of the proposed architecture.
• Figure 3: Visualization of synthetic multimodal graph signals.
• Figure 4: Original
• Figure 5: Observed (0.30)