Without a priori knowledge solving the interior problem in CT using two scans

Recently, region-of-interest (ROI) reconstruction problem has been solved exactly for imaging configurations satisfying some geometrical conditions, especially the interior problem while the ROI is totally contained inside the object. The exact reconstruction of the interior problem has been also proved to be theoretically possible under few restrictions. One of these restrictions is the requirement of a
priori
knowledge of the object on a limited region inside the ROI. However, this kind of a
priori
knowledge is not easily satisfied in practice. In the paper, we focus on solving the interior problem without a
priori
knowledge. A novel data sufficiency condition is presented that unique and stable interior ROI reconstruction can be obtained without a priori knowledge. It needs only the line integrals passing through this ROI and the other small FOV
₂
located outside the object. A reconstruction algorithm is developed which can be considered an extension of the DBP-POCS (differentiated backprojection-projection onto convex sets) method. Finally, we present experimental results using real data to illustrate the new data sufficiency condition and the good stability of the algorithm. In practice, the required projection data can be collected by two scans. In each scan, the FOV respectively covers the ROI and FOV
₂
by adjusting the X-ray beam width with a collimator, which can effectively reduce the detector area and radiation dose.