NOIR: Neural Operator mapping for Implicit Representations

2026-03-13

AI Summary

This work proposes a novel paradigm for medical image processing by modeling imaging tasks as operator learning between continuous function spaces, overcoming the limitations of traditional discrete-grid approaches that struggle with resolution-independent functional mappings. The method integrates implicit neural representations (INRs) to embed discrete signals and employs neural operators in a latent modulation space to achieve function-to-function mappings. It is the first to combine INRs with neural operators for multimodal medical imaging tasks, supporting segmentation, completion, translation, and synthesis in both 2D and 3D while preserving rigorous operator-theoretic properties. Experiments demonstrate state-of-the-art performance at native resolutions across multiple public and clinical datasets, along with strong robustness to unseen discretization schemes.

Technology Category

• Machine Learning: Multimodal Learning
• Computer Vision: Medical and Biological Imaging
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG

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.

Problem

• Neural Operator
• Implicit Representations
• Medical Imaging
• Resolution Independence
• Function Spaces

Innovation

• Neural Operator
• Implicit Neural Representations
• Function Space Learning
• Resolution Independence
• Medical Image Processing