A general region-of-interest image reconstruction approach with truncated Hilbert transform

This paper presents a novel data sufficiency condition that unique and stable ROI reconstruction can be achieved from a more flexible family of data sets. To the interior problem, it allows the ROI (Region-of-interest) can be reconstructed from the line integrals passing through this ROI and a small region B located anywhere as long as the image is known on B. Especially, ROI reconstruction can be achieved without any other a priori knowledge when region B is placed outside the object support. We also develop a general reconstruction algorithm with the DBP-POCS (Differentiated backprojection-projection onto convex sets) method. Finally, both numerical and real experiments were done to illustrate the new data sufficiency condition and the good stability of the ROI reconstruction algorithm.