Multimodal Signal Restoration with Signed Twofold Graph Learning
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913163935481856 |
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| author | Yokota, Haruki Higashi, Hiroshi Tanaka, Yuichi |
| author_facet | Yokota, Haruki Higashi, Hiroshi Tanaka, Yuichi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_26760 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Multimodal Signal Restoration with Signed Twofold Graph Learning Yokota, Haruki Higashi, Hiroshi Tanaka, Yuichi Signal Processing 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. |
| title | Multimodal Signal Restoration with Signed Twofold Graph Learning |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2605.26760 |