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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