Continuous Learned Primal Dual
This work addresses inverse problems in medical imaging for improved CT reconstruction, but it is incremental as it adapts existing methods to a new framework.
The authors tackled the problem of computed tomography (CT) reconstruction by applying Neural ODEs to the Learned Primal Dual algorithm, resulting in a continuous version that shows increased performance over discrete methods in imaging applications.
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.