Neural ordinary differential equations (Neural ODEs) propose the idea that a
sequence of layers in a neural network is just a discretisation of an ODE, and
thus can instead be directly modelled by a parameterised ODE. This idea has had
resounding success in the deep learning literature, with direct or indirect
influence in many state of the art ideas, such as diffusion models or time
dependant models. Recently, a continuous version of the U-net architecture has
been proposed, showing increased performance over its discrete counterpart in
many imaging applications and wrapped with theoretical guarantees around its
performance and robustness. In this work, we explore the use of Neural ODEs for
learned inverse problems, in particular with the well-known Learned Primal Dual
algorithm, and apply it to computed tomography (CT) reconstruction.

神经常微分方程（Neural ODEs）在深度学习文献中取得了巨大成功，最近提出了连续版本的 U-net 架构，在图像应用中显示出比离散版本更高的性能，并围绕其性能和鲁棒性提供了理论保证。本文探讨了使用神经 ODE 解决学习逆问题的可能性，尤其是在已知的学习 Primal Dual 算法中，并将其应用于 CT 重建。