Work

Equivariant Splitting: Self-supervised learning from incomplete data

Year: 2025

Type: preprint

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

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2510.00929

Authors: Sechaud, Victor, Scanvic, Jérémy, Barthélemy, Quentin, Abry, Patrice, Tachella, Julián

Institutions: École Normale Supérieure de Lyon, Centre National de la Recherche Scientifique, Laboratoire de Physique de l'ENS de Lyon

Language: English

Topic: Image and Signal Denoising Methods

Subfield: Computer Vision and Pattern Recognition

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: Agence Nationale de la Recherche, Grand Équipement National De Calcul Intensif, École Normale Supérieure de Lyon

Award: Unsupervised Learning for Non-Linear Inverse Problems

OpenAlex ID: W4414820712

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