3D Region-of-Interest (ROI) Reconstruction from Truncated Data in Circular Cone-beam CT

The circular cone-beam CT is one of the most widely adopted data-acquisition configurations in clinical and industrial applications, because it makes use of X-ray more effectively and shortens the scanning time. Among many algorithms for cone-beam circular scans, the FDK algorithm is the most widely used algorithm. It gives reasonably good results for small cone angle CT in case of no truncation in transverse direction, i.e., the cone beam covers the whole object in the full circular scan. When data contain transverse truncations, FDK algorithm may reconstruct images with significant truncation artifacts. Considering the importance of circular cone-beam scans in applications, in this paper we focus on a practically significant topic to reconstruct 3D ROI images from truncated circular cone-beam data. We expect the ROI images are free of truncation artifacts and comparable to the results obtained from nontruncated cone-beam data. Bade on the recent works, we summarize and develop a general 3D ROI reconstruction approach based on truncated Hilbert transform on PI-line segments. Backprojection-filtration (BPF) algorithm is combined with the method of iterated projections on convex sets (POCS) to invert the truncated Hilbert transform along a family of PI-line segments covering the ROI. In each iterative step, total variation (TV) method is used to denoising and optimizing the reconstructed 3D images in order to improve the iterative convergence speed. A novel data sufficiency condition is also presented that unique ROI reconstruction can be achieved from a more flexible family of data sets. For the interior problem, it shows the interior ROI can be reconstructed from the line integrals passing through not only this ROI but also another small region B located outside the object or on the edge of the object. It doesn't require any other a priori knowledge. Computer-simulation studies were done to validate and evaluate the proposed 3D region-of-interest (ROI) imaging approach from truncated data in circular cone-beam CT