Multimodadl graph signal denoising with simultaneous graph learning using deep algorithm unrolling

We propose a simultaneous method of multimodal graph signal denoising and graph learning. Since sensor networks distributed in space can capture multiple modalities of data, referred to as modalities, they are assumed to have an underlying structure or correlations both in space and modality. Such multimodal data are regarded as graph signals on a twofold graph. Like regular signals, multimodal graph signals can be corrupted by noise during their sensing process. Furthermore, their spatial/modality relationships are not given a priori: We need to estimate twofold graphs during denoising. In this paper, we propose a signal denoising method on twofold graphs where graphs are learned simultaneously. Specifically, we formulate an optimization problem for that, and an iterative algorithm for solving it is unrolled with deep algorithm unrolling (DAU). In the proposed method, the parameters in iterations are learned from training data that results in faster convergence and denoising quality improvements. Experimental results demonstrate that the proposed method outperforms existing graph signal denoising methods.