{"ID":2862112,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.00929","arxiv_id":"2510.00929","title":"Equivariant Splitting: Self-supervised learning from incomplete data","abstract":"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","short_abstract":"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-...","url_abs":"https://arxiv.org/abs/2510.00929","url_pdf":"https://arxiv.org/pdf/2510.00929v6","authors":"[\"Victor Sechaud\",\"Jérémy Scanvic\",\"Quentin Barthélemy\",\"Patrice Abry\",\"Julián Tachella\"]","published":"2025-10-01T14:08:17Z","proceeding":"cs.CV","tasks":"[\"cs.CV\"]","methods":"[]","has_code":false,"code_links":[{"ID":608873,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_id":2862112,"paper_url":"https://arxiv.org/abs/2510.00929","paper_title":"Equivariant Splitting: Self-supervised learning from incomplete data","repo_url":"https://github.com/vsechaud/Equivariant-Splitting","is_official":false,"mentioned_in_paper":false,"mentioned_in_github":true,"github_stars":0}]}