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Abstract:We propose a method for jointly learning signed twofold graphs and performing signal restoration on multimodal graph signals. 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 as follows. To learn twofold graphs from noisy and incomplete data, we formulate 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). To capture negative inter-modal correlations, we 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 two real-world datasets (Japan meteorological and Beijing air-quality data) confirm that the proposed method outperforms existing baselines across a range of noise levels and missing-data patterns; the learned graphs are also directly validated against the ground-truth graphs on the synthetic datasets.

Submission history

From: Haruki Yokota [view email]
[v1] Tue, 26 May 2026 09:31:05 UTC (4,692 KB)
[v2] Mon, 14 Sep 2026 04:28:30 UTC (2,821 KB)