Multimodal Graph Signal Denoising Via Twofold Graph Smoothness Regularization with Deep Algorithm Unrolling

We propose a denoising method of multimodal graph signals with twofold smoothness regularization. Graph signal processing assumes that a signal has an underlying structure that is represented by a graph. In each node of the graph, we often have multimodal data or features that are correlated across modalities. Since these multimodal data are measured by various sensors, the observed data will be noisy. In this paper, we assume that a multimodal signal is smooth on two underlying graphs: One is a spatial graph (i.e., relationship among nodes) and the other is a modality graph (i.e., relationship among modalities). We formulate a regularized minimization problem based on smoothness on the twofold graphs. The problem is solved with an alternating minimization scheme. To avoid a hand-crafted parameter tuning that is usually costly and converges to local minima, we utilize deep algorithm unrolling (DAU) to train the parameters in the algorithm. To validate the proposed method, we conduct experiments on synthetic data and demonstrate that our method outperforms various existing graph signal denoising methods.