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.

本文提出了一种称为“稳健等变成像”（REI）的框架，利用Stein的无偏风险估计器（SURE）实现对噪声具有鲁棒性的全面无人监督训练，从而在对抗噪声的情况下提高了线性和非线性反问题的性能表现，为深度网络的稳健无人监督成像铺平了道路。

稳健等变成像：一种完全无监督的框架，用于从噪声和部分测量中学习成像