Data consistency condition for truncated projections in fan-beam geometry

• Published in: Journal of X-ray science and technology Vol. 23; no. 5; pp. 627 - 638
• Main Authors: Yu, Hengyong, Wang, Ge, Yang, Jiansheng, Pack, Jed D., Jiang, Ming, De Man, Bruno
• Format: Journal Article
• Language: English
• Published: London, England SAGE Publications 21.09.2015
• Subjects: Computer Simulation; Humans; Image Processing, Computer-Assisted - methods; Phantoms, Imaging; Tomography, X-Ray Computed - methods; fan-beam geometry; Data consistency condition; truncated projections; general scanning trajectory; interior problem; motion artifact reduction
• ISSN: 0895-3996; 1095-9114
• DOI: 10.3233/XST-150515

It is well known that CT projections are redundant. Over the past decades, significant efforts have been devoted to characterize the data redundancy in different aspects. Very recently, Clackdoyle and Desbat reported a new integral-type data consistency condition (DCC) for truncated 2D parallel-beam projections, which can be applied to a region inside a field of view (FOV) but outside of the convex hull of the compact support of an object. Inspired by their work, here we derive a more general condition for 2D fan-beam geometry with a general scanning trajectory. This extended DCC is verified with simulated projections of the Shepp-Logan phantom and a clinically collected sinogram. Then, we demonstrate an application of the proposed DCC.