Robust Equivariant Imaging: a fully unsupervised framework for learning to image from noisy and partial measurements
2021
Deep networks provide state-of-the-art performance in multiple imaging
inverse problems ranging from medical imaging to computational photography.
However, most existing networks are trained with clean signals which are often
hard or impossible to obtain. Equivariant imaging (EI) is a recent
self-supervised learning framework that exploits the group invariance present
in signal distributions to learn a reconstruction function from partial
measurement data alone. While EI results are impressive, its performance
degrades with increasing noise. In this paper, we propose a Robust Equivariant
Imaging (REI) framework which can learn to image from noisy partial
measurements alone. The proposed method uses Stein's Unbiased Risk Estimator
(SURE) to obtain a fully unsupervised training loss that is robust to noise. We
show that REI leads to considerable performance gains on linear and nonlinear
inverse problems, thereby paving the way for robust unsupervised imaging with
deep networks. Code will be available at: https://github.com/edongdongchen/REI.
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