用神经算子实现医学影像的连续函数映射，支持分辨率无关处理。
NOIR: Neural Operator mapping for Implicit Representations
- 将医学影像任务建模为函数空间间的算子学习，避免离散网格限制。
- 在多个数据集上达到与原生分辨率相当的性能，且对未见采样率鲁棒。
- 适用于需高保真、跨分辨率处理的医学图像分析场景。
本文提出NOIR框架，将核心医学影像任务重新定义为连续函数空间间的算子学习，挑战现有基于离散网格的深度学习范式。不同于固定像素或体素网格的处理方式，NOIR将离散医学信号嵌入共享的隐式神经表示，并学习映射其潜在调制的神经算子，实现分辨率无关的函数到函数变换。我们在多个2D和3D下游任务（包括分割、形状补全、图像到图像转换、图像合成）上评估NOIR，使用Shenzhen、OASIS-4、SkullBreak、fastMRI及内部临床数据集。结果表明，NOIR在原生分辨率下表现优异，对未见离散化具有强鲁棒性，并经验性满足神经算子的关键理论性质。
原文摘要 · Abstract (English)
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.
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