  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.
