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.

提出了一种利用神经辐射场（NeRF）概念的新型亚采样磁共振成像（MRI）技术，通过径向亚采样，将相应的成像问题转化为从稀疏观察数据渲染的图像建模任务，因此可以利用隐式神经表示从亚采样的 K 空间数据中获得高维 MR 图像。