In this work, we propose Regularization-by-Equivariance (REV), a novel structure-adaptive regularization scheme for solving imaging inverse problems under incomplete measurements. Our 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. Our 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,用以在不完全的测量条件下解决成像反问题。我们的正规化计划利用测量物理学的等同结构结构 -- -- 这在许多反常问题中普遍存在,如图像成像重建等,以减轻反向问题的不正确性。我们提议的计划可以与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。我们在稀有的X射线图像重建任务中进行的数字实验证明了我们的方法的有效性。