Phase-contrast tomography and the local tomography problem

Phase-contrast tomography is a non-interferometric imaging technique for reconstructing the refractive index distribution of a weakly absorbing object from a set of tomographic projection measurements. In many practical situations, it is desirable to minimize the field of view (FOV) of the imaging system in order to increase the spatial resolution of the reconstructed image. When the object of interest is larger than the FOV, the measured projections are truncated and one is faced with a local tomography reconstruction problem. In this work, we investigate the local tomography problem for phase-contrast tomography and propose a simple algorithm for reconstructing image boundaries from untruncated and truncated phase-contrast projection data. Simulation studies are presented to corroborate our theoretical findings.