Continuous Learned Primal Dual

TL;DR

This paper explores the application of Neural ODEs to inverse problems, specifically using the Learned Primal Dual algorithm for improved CT reconstruction, leveraging continuous deep learning models for enhanced performance and robustness.

Contribution

It introduces a continuous Neural ODE-based approach to the Learned Primal Dual algorithm for CT reconstruction, combining continuous modeling with inverse problem solving.

Findings

Improved CT reconstruction quality using Neural ODEs

Enhanced robustness and performance over traditional methods

Demonstrated effectiveness in inverse problem settings

Abstract

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.