IOP PUBLISHING PHYSICS IN MEDICINE AND BIOLOGY Phys. Med. Biol. 52 (2007) R1–R13 doi:10.1088/0031-9155/52/6/R01 TOPICAL REVIEW Approximate and exact cone-beam reconstruction with standard and non-standard spiral scanning Ge Wang 1,2 , Yangbo Ye 3 and Hengyong Yu 1 1 Biomedical Imaging Division, VT-WFU School of Biomedical Engineering, Virginia Tech, Blacksburg, VA 24061, USA 2 Biomedical Imaging Division, VT-WFU School of Biomedical Engineering, Wake Forest University, Winston-Salem, NC 27157, USA 3 Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA E-mail: wangg@vt.edu, yangbo-ye@uiowa.edu and hengyongyu@vt.edu Received 1 October 2006, in final form 30 November 2006 Published 19 February 2007 Online at stacks.iop.org/PMB/52/R1 Abstract The long object problem is practically important and theoretically challenging. To solve the long object problem, spiral cone-beam CT was first proposed in 1991, and has been extensively studied since then. As a main feature of the next generation medical CT, spiral cone-beam CT has been greatly improved over the past several years, especially in terms of exact image reconstruction methods. Now, it is well established that volumetric images can be exactly and efficiently reconstructed from longitudinally truncated data collected along a rather general scanning trajectory. Here we present an overview of some key results in this area. 1. Introduction In x-ray computed tomography (CT), projections are typically collected from a source trajectory around an object to be reconstructed. In the 2D case, the fan-beam geometry is the most common, which is defined by a point source and a linear detector array. In the 3D case, cone-beam geometry becomes more and more popular with use of an area detector array. As compared to fan-beam geometry, cone-beam geometry allows 2D data acquisition, large volume coverage and efficient photon utilization. When the object is spherical, cone-beam projections can often be collected from various orientations without any data truncation. However, when the object is rather long, cone-beam projections are longitudinally truncated in many applications due to limitations in detector extent and radiation dose. This long object problem is practically very important. In material science and engineering, specimens are often rod shaped. In medical imaging, patients are quite long. In small animal imaging, mice and rats are fairly similar to the human in terms of anatomical proportions. 0031-9155/07/060001+13$30.00 © 2007 IOP Publishing Ltd Printed in the UK R1