  Limited-angle and sparse-view computed tomography (LACT and SVCT) are crucial
for expanding the scope of X-ray CT applications. However, they face challenges
due to incomplete data acquisition, resulting in diverse artifacts in the
reconstructed CT images. Emerging implicit neural representation (INR)
techniques, such as NeRF, NeAT, and NeRP, have shown promise in
under-determined CT imaging reconstruction tasks. However, the unsupervised
nature of INR architecture imposes limited constraints on the solution space,
particularly for the highly ill-posed reconstruction task posed by LACT and
ultra-SVCT. In this study, we introduce the Diffusion Prior Driven Neural
Representation (DPER), an advanced unsupervised framework designed to address
the exceptionally ill-posed CT reconstruction inverse problems. DPER adopts the
Half Quadratic Splitting (HQS) algorithm to decompose the inverse problem into
data fidelity and distribution prior sub-problems. The two sub-problems are
respectively addressed by INR reconstruction scheme and pre-trained score-based
diffusion model. This combination first injects the implicit image local
consistency prior from INR. Additionally, it effectively augments the
feasibility of the solution space for the inverse problem through the
generative diffusion model, resulting in increased stability and precision in
the solutions. We conduct comprehensive experiments to evaluate the performance
of DPER on LACT and ultra-SVCT reconstruction with two public datasets (AAPM
and LIDC), an in-house clinical COVID-19 dataset and a public raw projection
dataset created by Mayo Clinic. The results show that our method outperforms
the state-of-the-art reconstruction methods on in-domain datasets, while
achieving significant performance improvements on out-of-domain (OOD) datasets.
