Space-Filling X-Ray Source Trajectories for Efficient Scanning in Large-Angle Cone-Beam Computed Tomography

We present a new family of X-ray source scanning trajectories for large-angle cone-beam computed tomography. Traditional scanning trajectories are described by continuous paths through space, e.g., circles, saddles, or helices, with a large degree of redundant information in adjacent projection images. Here, we consider discrete trajectories as a set of points that uniformly sample the entire space of possible source positions, i.e., a space-filling trajectory (SFT). We numerically demonstrate the advantageous properties of the SFT when compared with circular and helical trajectories as follows: first, the most isotropic sampling of the data, second, optimal level of mutually independent data, and third, an improved condition number of the tomographic inverse problem. The practical implications of these properties in tomography are also illustrated by simulation. We show that the SFT provides greater data acquisition efficiency, and reduced reconstruction artifacts when compared with helical trajectory. It also possesses an effective preconditioner for fast iterative tomographic reconstruction.