Compressive sensing is a method to recover the original image from
undersampled measurements. In order to overcome the ill-posedness of this
inverse problem, image priors are used such as sparsity in the wavelet domain,
minimum total-variation, or self-similarity. Recently, deep learning based
compressive image recovery methods have been proposed and have yielded
state-of-the-art performances. They used deep learning based data-driven
approaches instead of hand-crafted image priors to solve the ill-posed inverse
problem with undersampled data. Ironically, training deep neural networks for
them requires "clean" ground truth images, but obtaining the best quality
images from undersampled data requires well-trained deep neural networks. To
resolve this dilemma, we propose novel methods based on two well-grounded
theories: denoiser-approximate message passing and Stein's unbiased risk
estimator. Our proposed methods were able to train deep learning based image
denoisers from undersampled measurements without ground truth images and
without image priors, and to recover images with state-of-the-art qualities
from undersampled data. We evaluated our methods for various compressive
sensing recovery problems with Gaussian random, coded diffraction pattern, and
compressive sensing MRI measurement matrices. Our methods yielded
state-of-the-art performances for all cases without ground truth images and
without image priors. They also yielded comparable performances to the methods
with ground truth data.

本文提出基于去噪 - 近似传递消息和 Stein 无偏风险估计器理论的新方法，用于训练深度学习图像去噪器。这些方法能够从少量观测数据中恢复高质量图像，不需要原始图像，也不需要手动设置的图像先验条件，并在各种具有挑战性的压缩感知恢复问题上实现了最先进的性能。