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.

翻译：在这项工作中,我们建议实行按部就班的正规化(REV),这是一个新颖的结构适应性正规化计划,用于解决测量不完全情况下的成像反问题。这个正规化计划利用测量物理学的等同结构结构 -- -- 这种结构在许多反常问题中普遍存在,如图像图像重建等,以减轻反向问题的不正确性。我们提议的计划可以用插座和游戏方式与任何典型的第一阶优化算法(如加速梯度下降/FISTA)一起应用,以简单和快速趋同。稀有的X射线图像重建任务的数字实验显示了我们的方法的有效性。