Equivariance Regularization for Image Reconstruction
- URL: http://arxiv.org/abs/2202.05062v2
- Date: Sat, 12 Feb 2022 15:30:04 GMT
- Title: Equivariance Regularization for Image Reconstruction
- Authors: Junqi Tang
- Abstract summary: We propose a 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 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.
- Score: 5.025654873456756
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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.
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