Algorithm Unrolling-based Denoising of Multimodal Graph Signals

TL;DR

This paper introduces a novel deep unrolling-based method for denoising multimodal graph signals, simultaneously learning the underlying twofold graph structure and restoring signals.

Contribution

It proposes a new algorithm that combines alternating minimization, primal-dual splitting, and deep unrolling to improve multimodal graph signal denoising.

Findings

Outperforms existing graph signal denoising methods on synthetic data.

Effectively learns twofold graph structures during denoising.

Demonstrates superior performance on real-world multimodal data.

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.