This article presents a novel undersampled magnetic resonance imaging (MRI) technique that leverages the concept of Neural Radiance Field (NeRF). With radial undersampling, the corresponding imaging problem can be reformulated into an image modeling task from sparse-view rendered data; therefore, a high dimensional MR image is obtainable from undersampled k-space data by taking advantage of implicit neural representation. A multi-layer perceptron, which is designed to output an image intensity from a spatial coordinate, learns the MR physics-driven rendering relation between given measurement data and desired image. Effective undersampling strategies for high-quality neural representation are investigated. The proposed method serves two benefits: (i) The learning is based fully on single undersampled k-space data, not a bunch of measured data and target image sets. It can be used potentially for diagnostic MR imaging, such as fetal MRI, where data acquisition is relatively rare or limited against diversity of clinical images while undersampled reconstruction is highly demanded. (ii) A reconstructed MR image is a scan-specific representation highly adaptive to the given k-space measurement. Numerous experiments validate the feasibility and capability of the proposed approach.

翻译：本文提出了一种新颖的欠采样磁共振成像（MRI）技术，利用神经辐射场（NeRF）的概念。通过径向欠采样，相应的成像问题可重新表述为从稀疏视角渲染数据中的图像建模任务；因此，利用隐式神经表示，可从欠采样k空间数据中获取高维MR图像。一个多层感知器被设计用于从空间坐标输出图像强度，学习给定测量数据与目标图像之间由MR物理驱动的渲染关系。本文研究了用于高质量神经表示的有效欠采样策略。所提方法具有两大优势：（i）学习过程完全基于单个欠采样k空间数据，而非大量测量数据与目标图像集。该方法可潜在地用于诊断性MR成像，例如胎儿MRI——此类场景下数据采集相对稀少或受限于临床图像的多样性，而对欠采样重建的需求极高。（ii）重建的MR图像是一种高度适应给定k空间测量的扫描特异性表示。大量实验验证了所提方法的可行性与能力。