Interior tomography using the truncated Hilbert transform with the total variation constraint

Interior tomography is to reconstruct the interior region of interest (ROI) from the projection data just across the ROI. One kind of interior reconstruction methods is based on the inversion of truncated Hilbert transform (THT) when there is a known sub-region inside ROI. However, the result via this method is usually to be degraded by noise in real data case. In this paper, we propose to incorporate the total variation (TV) minimization constraint into the THT-based interior tomography to improve the reconstruction quality. Therein, we first carry out projection-on-convex-sets (POCS) iteration on each chord, and then we perform a soft-threshold based TV minimization on the intermediate image. In order to validate the proposed method, we conduct both simulated and real data experiments. The results show that with TV constraint the proposed method can lead to better ROI with less noise.