New algorithm speeds X-ray scattering reconstruction 10x for real-time 3D imaging

X-ray scattering tensor tomography reveals 3D nanoscale structural orientation but has been limited by slow iterative reconstruction methods, preventing real-time use. In a new arXiv preprint (2607.19124), André M. Antunes and colleagues introduce a direct reconstruction algorithm for parallel-beam geometries that computes algebraic filters to approximate multiple iterative updates in a single filtering and back-projection step. By explicitly separating the tomographic projector from a view-dependent mixing operator, the method generalizes across different tensor representations and small-angle X-ray scattering measurement modes.

The researchers validated their approach using both simulated and experimental data, showing that the direct reconstruction closely matches iterative results while reducing computational time by over an order of magnitude. A 53×53×53×28 tensor volume can be reconstructed in just 1 second on commercially available hardware, compared to many minutes or hours with iterative methods. This speed and stability open the door to real-time scattering-based imaging, enabling high-throughput analysis in materials science, biology, and non-destructive testing where nanoscale orientation information is critical.