NOIR: Neural Operator mapping for Implicit Representations

TL;DR

NOIR introduces a novel operator learning framework for medical imaging that operates on continuous function spaces, enabling resolution-independent transformations and robust performance across various tasks and datasets.

Contribution

It proposes a new paradigm of using neural operators with implicit representations for medical imaging, moving beyond traditional grid-based methods.

Findings

Achieves competitive results on multiple medical imaging tasks.

Demonstrates robustness to different discretizations.

Satisfies key theoretical properties of neural operators.

Abstract

This paper presents NOIR, a framework that reframes core medical imaging tasks as operator learning between continuous function spaces, challenging the prevailing paradigm of discrete grid-based deep learning. Instead of operating on fixed pixel or voxel grids, NOIR embeds discrete medical signals into shared Implicit Neural Representations and learns a Neural Operator that maps between their latent modulations, enabling resolution-independent function-to-function transformations. We evaluate NOIR across multiple 2D and 3D downstream tasks, including segmentation, shape completion, image-to-image translation, and image synthesis, on several public datasets such as Shenzhen, OASIS-4, SkullBreak, fastMRI, as well as an in-house clinical dataset. It achieves competitive performance at native resolution while demonstrating strong robustness to unseen discretizations, and empirically satisfies key theoretical properties of neural operators. The project page is available here: https://github.com/Sidaty1/NOIR-io.