  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, which do not apply to
all the samples in XDT. Here we propose a quasi-interior XDT scheme that
incorporates a small fraction of projection information from the exterior
region to assist interior reconstruction. The low-resolution exterior
projection data obviates the requirement for prior knowledge on the object, and
allows the ROI reconstruction to be performed with the fast, widely-used
filtered back-projection algorithm for easy integration into real-time XDT
imaging modules.
