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.

翻译：本文提出NOIR框架，该框架将核心医学影像任务重新定义为连续函数空间之间的算子学习问题，从而挑战了当前主流的基于离散网格的深度学习范式。与在固定像素或体素网格上操作不同，NOIR将离散医学信号嵌入到共享的隐式神经表示中，并学习一个在它们的潜在调制之间进行映射的神经算子，从而实现与分辨率无关的函数到函数变换。我们在多个公开数据集（如Shenzhen、OASIS-4、SkullBreak、fastMRI）以及内部临床数据集上，通过包括分割、形状补全、图像到图像转换和图像合成在内的多种2D与3D下游任务对NOIR进行评估。该方法在原始分辨率下取得了具有竞争力的性能，同时对未见过的离散化方案表现出强大的鲁棒性，并在经验上满足了神经算子的关键理论性质。项目页面详见：https://github.com/Sidaty1/NOIR-io。