MRI Image Reconstruction via Learning Optimization Using Neural ODEs

TL;DR

This paper introduces a novel MRI image reconstruction method that models the optimization process as a neural ODE, leading to improved results and efficiency over traditional neural network approaches.

Contribution

It formulates MRI reconstruction as a neural ODE-based optimization process, incorporating learned solvers for better accuracy and efficiency compared to existing methods.

Findings

Neural ODE models outperform UNet and cascaded CNN in reconstruction quality.

Incorporating learned solvers enhances model performance and parameter efficiency.

The approach offers a new perspective by modeling continuous optimization dynamics for MRI reconstruction.

Abstract

We propose to formulate MRI image reconstruction as an optimization problem and model the optimization trajectory as a dynamic process using ordinary differential equations (ODEs). We model the dynamics in ODE with a neural network and solve the desired ODE with the off-the-shelf (fixed) solver to obtain reconstructed images. We extend this model and incorporate the knowledge of off-the-shelf ODE solvers into the network design (learned solvers). We investigate several models based on three ODE solvers and compare models with fixed solvers and learned solvers. Our models achieve better reconstruction results and are more parameter efficient than other popular methods such as UNet and cascaded CNN. We introduce a new way of tackling the MRI reconstruction problem by modeling the continuous optimization dynamics using neural ODEs.