  Self-supervised methods have recently proved to be nearly as effective as
supervised methods in various imaging inverse problems, paving the way for
learning-based methods in scientific and medical imaging applications where
ground truth data is hard or expensive to obtain. This is the case in magnetic
resonance imaging and computed tomography. These methods critically rely on
invariance to translations and/or rotations of the image distribution to learn
from incomplete measurement data alone. However, existing approaches fail to
obtain competitive performances in the problems of image super-resolution and
deblurring, which play a key role in most imaging systems. In this work, we
show that invariance to translations and rotations is insufficient to learn
from measurements that only contain low-frequency information. Instead, we
propose a new self-supervised approach that leverages the fact that many image
distributions are approximately scale-invariant, and that can be applied to any
inverse problem where high-frequency information is lost in the measurement
process. We demonstrate throughout a series of experiments on real datasets
that the proposed method outperforms other self-supervised approaches, and
obtains performances on par with fully supervised learning.

Image and Video Processing;Computer Vision and Pattern Recognition