PI-Line Difference for Alignment and Motion-Correction of Cone-Beam Helical-Trajectory Micro-Tomography Data

In micro-tomography, variants of helical X-ray source trajectories, e.g., double-helix (DH) and space-filling (SF), are attractive alternatives to the conventional circular trajectory, as they satisfy data-sufficiency conditions; this enables exact reconstruction, and large cone-angle (or high flux) imaging. Geometric alignment of micro-tomography experimental data, i.e., radiographs or projection data, to the required micron precision is a difficult problem. In this paper, we consider criteria based on differences in attenuation along opposing rays as a postacquisition software alignment technique. These opposing rays are called PI-lines and lie on lines that intersect two points of the scanning trajectory and pass through the region of support. The PI-line difference method is particularly appealing due to its low computational cost and small set of inherent assumptions, however, previous studies have exposed some limitations in precision. The number and distribution of PI-lines is highly dependent on the trajectory and thus so is the robustness of PI-line difference; here we show that DH and SF trajectories are particularly amenable to this technique. For these trajectories, we observe that the technique is applicable to both static and per-projection alignment estimation. We present results where PI-line difference alignment estimates are of equivalent accuracy as alignment estimates obtained from existing state-of-the-art methods: a tomogram sharpness method for static alignment and a reprojection-alignment method for per-projection alignment. In both cases, the computational expense of PI-line difference alignment estimation is a fraction of the tomogram-based methods.