  In this work, we propose Regularization-by-Equivariance (REV), a novel
structure-adaptive regularization scheme for solving imaging inverse problems
under incomplete measurements. This regularization scheme utilizes the
equivariant structure in the physics of the measurements -- which is prevalent
in many inverse problems such as tomographic image reconstruction -- to
mitigate the ill-poseness of the inverse problem. Our proposed scheme can be
applied in a plug-and-play manner alongside with any classic first-order
optimization algorithm such as the accelerated gradient descent/FISTA for
simplicity and fast convergence. The numerical experiments in sparse-view X-ray
CT image reconstruction tasks demonstrate the effectiveness of our approach.
