Equivariant Splitting: Self-supervised learning from incomplete data

• URL: http://arxiv.org/abs/2510.00929v3
• Date: Fri, 03 Oct 2025 17:59:18 GMT
• Title: Equivariant Splitting: Self-supervised learning from incomplete data
• Authors: Victor Sechaud, Jérémy Scanvic, Quentin Barthélemy, Patrice Abry, Julián Tachella,
• Abstract summary: We propose a new self-supervised learning strategy devised for the challenging setting where measurements are observed via a single incomplete observation model.<n>We show that the combination of self-supervised splitting losses and equivariant reconstruction networks results in the same minimizer in expectation as the one of a supervised loss.
• Score: 11.641086974203924
• License: http://creativecommons.org/licenses/by/4.0/
• 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 the same minimizer in expectation as the one of a supervised loss. Through a series of experiments on image inpainting, accelerated magnetic resonance imaging, and compressive sensing, we demonstrate that the proposed loss achieves state-of-the-art performance in settings with highly rank-deficient forward models.

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