Multimodal Signal Restoration with Signed Twofold Graph Learning

Abstract

Multimodal signals on sensor networks are commonly modeled under the twofold graph assumption (TGA), which represents spatial structure and inter-modality relations as two separate graphs. Existing TGA-based signal restoration methods, however, either assume the graphs are known or restrict edge weights to be non-negative, preventing them from capturing negative inter-modal correlations. We address both limitations by formulating joint signal restoration and twofold graph learning as MAP estimation under a matrix normal prior, where the spatial and modality graph Laplacians appear directly as precision matrices. The resulting non-convex objective is solved by alternating minimization: The signal is updated via conjugate gradient applied to the arising Sylvester-type linear system; the graphs are updated via primal-dual hybrid gradient (PDHG). We further propose a method to estimate the signed structure of the modality graph from the dominant eigenspace of a complementary kernel matrix, which is then used in PDHG to update edge magnitudes. These iterative solvers are then unrolled into a feedforward network, with regularization weights and step sizes as layer-wise trainable parameters. Experiments on synthetic multimodal graph signals and a real Japan meteorological dataset confirm that the proposed method outperforms existing baselines across a range of noise levels and missing-data patterns.