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International Journal of Biomedical Imaging
Volume 2006 (2006), Article ID 10427, 9 pages

A General Formula for Fan-Beam Lambda Tomography

CT/Micro-CT Laboratory, Department of Radiology, The University of Iowa, Iowa City, IA 52242, USA

Received 4 September 2005; Revised 12 November 2005; Accepted 12 November 2005

Academic Editor: Guowei Wei

Copyright © 2006 Hengyong Yu and Ge Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Lambda tomography (LT) is to reconstruct a gradient-like image of an object only from local projection data. It is potentially an important technology for medical X-ray computed tomography (CT) at a reduced radiation dose. In this paper, we prove the first general formula for exact and efficient fan-beam LT from data collected along any smooth curve based on even and odd data extensions. As a result, an LT image can be reconstructed without involving any data extension. This implies that structures outside a scanning trajectory do not affect the exact reconstruction of points inside the trajectory even if the data may be measured through the outside features. The algorithm is simulated in a collinear coordinate system. The results support our theoretical analysis.