  From early image processing to modern computational imaging, successful
models and algorithms have relied on a fundamental property of natural signals:
symmetry. Here symmetry refers to the invariance property of signal sets to
transformations such as translation, rotation or scaling. Symmetry can also be
incorporated into deep neural networks in the form of equivariance, allowing
for more data-efficient learning. While there has been important advances in
the design of end-to-end equivariant networks for image classification in
recent years, computational imaging introduces unique challenges for
equivariant network solutions since we typically only observe the image through
some noisy ill-conditioned forward operator that itself may not be equivariant.
We review the emerging field of equivariant imaging and show how it can provide
improved generalization and new imaging opportunities. Along the way we show
the interplay between the acquisition physics and group actions and links to
iterative reconstruction, blind compressed sensing and self-supervised
learning.
