  Incomplete-view computed tomography (CT) can shorten the data acquisition
time and allow scanning of large objects, including sparse-view and
limited-angle scenarios, each with various settings, such as different view
numbers or angular ranges. However, the reconstructed images present severe,
varying artifacts due to different missing projection data patterns. Existing
methods tackle these scenarios/settings separately and individually, which are
cumbersome and lack the flexibility to adapt to new settings. To enjoy the
multi-setting synergy in a single model, we propose a novel Prompted Contextual
Transformer (ProCT) for incomplete-view CT reconstruction. The novelties of
ProCT lie in two folds. First, we devise a projection view-aware prompting to
provide setting-discriminative information, enabling a single ProCT to handle
diverse incomplete-view CT settings. Second, we propose artifact-aware
contextual learning to sense artifact pattern knowledge from in-context image
pairs, making ProCT capable of accurately removing the complex, unseen
artifacts. Extensive experimental results on two publicly available clinical CT
datasets demonstrate the superior performance of ProCT over state-of-the-art
methods -- including single-setting models -- on a wide range of
incomplete-view CT settings, strong transferability to unseen datasets and
scenarios, and improved performance when sinogram data is available. The code
is available at: https://github.com/Masaaki-75/proct
