  Neural Radiance Field (NeRF) has widely received attention in Sparse-View
Computed Tomography (SVCT) reconstruction tasks as a self-supervised deep
learning framework. NeRF-based SVCT methods represent the desired CT image as a
continuous function of spatial coordinates and train a Multi-Layer Perceptron
(MLP) to learn the function by minimizing loss on the SV sinogram. Benefiting
from the continuous representation provided by NeRF, the high-quality CT image
can be reconstructed. However, existing NeRF-based SVCT methods strictly
suppose there is completely no relative motion during the CT acquisition
because they require \textit{accurate} projection poses to model the X-rays
that scan the SV sinogram. Therefore, these methods suffer from severe
performance drops for real SVCT imaging with motion. In this work, we propose a
self-calibrating neural field to recover the artifacts-free image from the
rigid motion-corrupted SV sinogram without using any external data.
Specifically, we parametrize the inaccurate projection poses caused by rigid
motion as trainable variables and then jointly optimize these pose variables
and the MLP. We conduct numerical experiments on a public CT image dataset. The
results indicate our model significantly outperforms two representative
NeRF-based methods for SVCT reconstruction tasks with four different levels of
rigid motion.
