Equivariant Splitting: Self-supervised learning from incomplete data
This addresses the challenge of training reconstruction networks without ground-truth data, which is beneficial for domains like medical imaging where obtaining references is costly or impossible.
The paper tackles the problem of self-supervised learning for inverse problems with incomplete data, proposing a method that combines equivariant reconstruction networks with splitting losses, achieving state-of-the-art performance in settings like image inpainting and accelerated MRI.
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.