There has been a renewed interest in algorithm development for image reconstruction from highly incomplete data in computed tomography (CT). Such algorithms may lead to reduced imaging dose and time, and to the design of innovative configurations tailored to specific imaging tasks. In recent years, a carbon-nanotube (CNT)-based field-emission x-ray source has been developed, which offers easy electronic control of radiation and thus can be an ideal candidate for gated imaging. We have recently proposed algorithms for image reconstruction from fan- and cone-beam data collected at highly sparse angular views through minimization of the total-variation (TV) of the image subject to the condition that the estimated data are consistent with the measured data. In this work, we investigate and demonstrate the application of the TV-minimization algorithm to reconstructing images from mouse data acquired with a CNT-based CT scanner at a number of views much lower than what is used in conventional CT imaging. The results demonstrate that the TV-minimization algorithm can yield images with quality comparable to those obtained from a large number of views by use of the conventional algorithms. The significance of the work may lie in that the substantial reduction of projection views promised by the TV-minimization algorithm can be exploited for reducing imaging dose and time or for improving temporal resolution in tasks such as dynamic imaging.

The back-projection-filtration (BPF) algorithm has been applied to image reconstruction for cone-beam configurations with general source trajectories. The BPF algorithm can reconstruct 3-D region-of-interest (ROI) images from data containing truncations. However, like many other existing algorithms for cone-beam configurations, the BPF algorithm involves a back-projection with a spatially varying weighting factor, which can result in the non-uniform noise levels in reconstructed images and increased computation time. In this work, we propose a BPF algorithm to eliminate the spatially varying weighting factor by using a rebinned geometry for a general scanning trajectory. This proposed BPF algorithm has an improved noise property, while retaining the advantages of the original BPF algorithm such as minimum data requirement.