Interior x-ray diffraction tomography with low-resolution exterior information

X-ray diffraction tomography (XDT) resolves spatially-variant XRD profiles within macroscopic objects, and provides improved material contrast compared to the conventional transmission-based computed tomography (CT). However, due to the small diffraction cross-section, XDT suffers from long imaging acquisition time, which could take tens of hours for a full scan using a table-top x-ray tube. In medical and industrial imaging applications, oftentimes only the XRD measurement within a region-of-interest (ROI) is required, which, together with the demand to reduce imaging time and radiation dose to the sample, motivates the development of interior XDT systems that scan and reconstruct only an internal region within the sample. The interior problem does not have a unique solution, and a direct inversion on the truncated projection data often leads to large reconstruction errors in ROI. To reduce the truncation artifacts, conventional attenuation-based interior reconstruction problems rely on a known region or piecewise constant constraint within the ROI. Here we propose a quasi-interior XDT scheme that incorporates a small fraction of projection information from the exterior region to assist ROI reconstruction. In the phantom simulation, a small amount (17% of exterior region) of added exterior projection data improves the reconstruction quality by ~50%. The addition of exterior samplings in the experiment demonstrates improved spatial and XRD profile reconstructions compared to total-variation-based reconstruction or sinogram extrapolation. We expect our quasi-interior XDT to obviate the requirement on prior knowledge of the object or its support, and to allow the ROI reconstruction to be performed with the fast, widely-used filtered back-projection algorithm for easy integration into real-time XDT imaging modules.