Equivariance Regularization for Image Reconstruction
This work addresses ill-posed inverse problems in imaging, such as tomographic reconstruction, with a plug-and-play method that is incremental in nature.
The paper tackled the problem of imaging inverse problems under incomplete measurements by proposing Regularization-by-Equivariance (REV), a structure-adaptive regularization scheme, and demonstrated its effectiveness in sparse-view X-ray CT image reconstruction tasks.
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.