  In various imaging problems, we only have access to compressed measurements
of the underlying signals, hindering most learning-based strategies which
usually require pairs of signals and associated measurements for training.
Learning only from compressed measurements is impossible in general, as the
compressed observations do not contain information outside the range of the
forward sensing operator. We propose a new end-to-end self-supervised framework
that overcomes this limitation by exploiting the equivariances present in
natural signals. Our proposed learning strategy performs as well as fully
supervised methods. Experiments demonstrate the potential of this framework on
inverse problems including sparse-view X-ray computed tomography on real
clinical data and image inpainting on natural images. Code will be released.
