Equivariant Splitting: Self-supervised learning from incomplete data
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914560253886464 |
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| author | Sechaud, Victor Scanvic, Jérémy Barthélemy, Quentin Abry, Patrice Tachella, Julián |
| author_facet | Sechaud, Victor Scanvic, Jérémy Barthélemy, Quentin Abry, Patrice Tachella, Julián |
| contents | Self-supervised learning for inverse problems allows to train a reconstruction network from noise and/or incomplete data alone. These methods have the potential of enabling learning-based solutions when obtaining ground-truth references for training is expensive or even impossible. In this paper, we propose a new self-supervised learning strategy devised for the challenging setting where measurements are observed via a single incomplete observation model. We introduce a new definition of equivariance in the context of reconstruction networks, and show that the combination of self-supervised splitting losses and equivariant reconstruction networks results in unbiased estimates of the supervised loss. Through a series of experiments on image inpainting, accelerated magnetic resonance imaging, sparse-view computed tomography, and compressive sensing, we demonstrate that the proposed loss achieves state-of-the-art performance in settings with highly rank-deficient forward models. The code is available at https://github.com/vsechaud/Equivariant-Splitting |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_00929 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equivariant Splitting: Self-supervised learning from incomplete data Sechaud, Victor Scanvic, Jérémy Barthélemy, Quentin Abry, Patrice Tachella, Julián Computer Vision and Pattern Recognition Self-supervised learning for inverse problems allows to train a reconstruction network from noise and/or incomplete data alone. These methods have the potential of enabling learning-based solutions when obtaining ground-truth references for training is expensive or even impossible. In this paper, we propose a new self-supervised learning strategy devised for the challenging setting where measurements are observed via a single incomplete observation model. We introduce a new definition of equivariance in the context of reconstruction networks, and show that the combination of self-supervised splitting losses and equivariant reconstruction networks results in unbiased estimates of the supervised loss. Through a series of experiments on image inpainting, accelerated magnetic resonance imaging, sparse-view computed tomography, and compressive sensing, we demonstrate that the proposed loss achieves state-of-the-art performance in settings with highly rank-deficient forward models. The code is available at https://github.com/vsechaud/Equivariant-Splitting |
| title | Equivariant Splitting: Self-supervised learning from incomplete data |
| topic | Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2510.00929 |