论文标题
图像重建的均衡正规化
Equivariance Regularization for Image Reconstruction
论文作者
论文摘要
在这项工作中，我们提出了正则化划分（REV），这是一种新型的结构自适应正规化方案，用于在不完整的测量中解决成像逆问题。这种正规化方案利用了测量物理学中的模棱两可的结构（在诸如层析成像图像重建等许多反问题中很普遍）来减轻反问题的不良对象。我们提出的方案可以与任何经典的一阶优化算法（例如加速梯度下降/Fista）一起以插件的方式应用，以简单和快速收敛。稀疏视图X射线CT图像重建任务中的数值实验证明了我们方法的有效性。
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.
