International Journal of Biomedical Imaging Development of Computed Tomography Algorithms Guest Editors: Hengyong Yu, Patrick J. La Riviere, and Xiangyang Tang International Journal of Biomedical Imaging Development of Computed Tomography Algorithms International Journal of Biomedical Imaging Development of Computed Tomography Algorithms Guest Editors: Hengyong Yu, Patrick J. La Riviere, and Xiangyang Tang Copyright © 2006 Hindawi Publishing Corporation. All rights reserved. This is a special issue published in volume 2006 of “International Journal of Biomedical Imaging.” All articles are open access articles distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Editor-in-Chief Ge Wang, Virginia Polytechnic Institute and State University, USA Associate Editors Haim Azhari, Israel Ming Jiang, China Jie Tian, China Kyongtae Bae, USA Marc Kachelrieß, Germany Michael Vannier, USA Richard Bayford, UK Seung Wook Lee, South Korea Yue Wang, USA Freek Beekman, The Netherlands Alfred Karl Louis, Germany Guowei Wei, USA Subhasis Chaudhuri, India Erik Meijering, The Netherlands David L. Wilson, USA Jyh-Cheng Chen, Taiwan Vasilis Ntziachristos, USA Sun Guk Yu, South Korea Anne Clough, USA Scott Pohlman, USA Habib Zaidi, Switzerland Carl Crawford, USA Erik Ritman, USA Yantian Zhang, USA Min Gu, Australia Jay Rubinstein, USA Yibin Zheng, USA Eric Hoffman, USA Pete Santago, USA Tiange Zhuang, China Jiang Hsieh, USA Lizhi Sun, USA Contents Development of Computed Tomography Algorithms, Hengyong Yu, Patrick J. La Rivière, and Xiangyang Tang Volume 2006 (2006), Article ID 39397, 3 pages Parallel Implementation of Katsevich's FBP Algorithm, Jiansheng Yang, Xiaohu Guo, Qiang Kong, Tie Zhou, and Ming Jiang Volume 2006 (2006), Article ID 17463, 8 pages Local ROI Reconstruction via Generalized FBP and BPF Algorithms along More Flexible Curves, Hengyong Yu, Yangbo Ye, Shiying Zhao, and Ge Wang Volume 2006 (2006), Article ID 14989, 7 pages An Approximate Cone Beam Reconstruction Algorithm for Gantry-Tilted CT Using Tangential Filtering, Ming Yan, Cishen Zhang, and Hongzhu Liang Volume 2006 (2006), Article ID 29370, 8 pages FDK Half-Scan with a Heuristic Weighting Scheme on a Flat Panel Detector-Based Cone Beam CT (FDKHSCW), Dong Yang and Ruola Ning Volume 2006 (2006), Article ID 83983, 8 pages Analysis of Cone-Beam Artifacts in off-Centered Circular CT for Four Reconstruction Methods, S. Valton, F. Peyrin, and D. Sappey-Marinier Volume 2006 (2006), Article ID 80421, 8 pages Extending Three-Dimensional Weighted Cone Beam Filtered Backprojection (CB-FBP) Algorithm for Image Reconstruction in Volumetric CT at Low Helical Pitches, Xiangyang Tang, Jiang Hsieh, Roy A. Nilsen, and Scott M. McOlash Volume 2006 (2006), Article ID 45942, 8 pages Comparison of Lesion Detection and Quantification in MAP Reconstruction with Gaussian and Non-Gaussian Priors, Jinyi Qi Volume 2006 (2006), Article ID 87567, 10 pages Comparison of Quadratic- and Median-Based Roughness Penalties for Penalized-Likelihood Sinogram Restoration in Computed Tomography, Patrick J. La Rivière, Junguo Bian, and Phillip A. Vargas Volume 2006 (2006), Article ID 41380, 7 pages A Prospective Study on Algorithms Adapted to the Spatial Frequency in Tomography, Vincent Israel-Jost, Philippe Choquet, and André Constantinesco Volume 2006 (2006), Article ID 34043, 6 pages Assessment of Left Ventricular Function in Cardiac MSCT Imaging by a 4D Hierarchical Surface-Volume Matching Process, Mireille Garreau, Antoine Simon, Dominique Boulmier, Jean-Louis Coatrieux, and Hervé Le Breton Volume 2006 (2006), Article ID 37607, 10 pages Hindawi Publishing Corporation International Journal of Biomedical Imaging Volume 2006, Article ID 39397, Pages 1–3 DOI 10.1155/IJBI/2006/39397 Editorial Development of Computed Tomography Algorithms Hengyong Yu,1 Patrick J. La Riviere,` 2 and Xiangyang Tang3 1 Department of Radiology, University of Iowa, Iowa City, IA 52242, USA 2 Department of Radiology, University of Chicago, Chicago, IL 60637, USA 3 Applied Science Laboratory, GE Healthcare, Waukesha, WI 53188, USA Received 31 May 2006; Accepted 31 May 2006 Copyright © 2006 Hengyong Yu et al. 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. Over the past several years, computed tomography (CT) heuristically adapted the fan-beam FBP algorithm for ap- methods have advanced significantly, yielding novel ana- proximate cone-beam reconstruction in the case of a circu- lytic and iterative solutions applicable to medical CT and lar scanning locus [5]. This formulation, called the FDK al- micro-CT. The resulting algorithms promise to improve spa- gorithm, is more desirable in many cases than exact cone- tial, contrast, or temporal resolution as well as to suppress beam reconstruction approaches in terms of several aspects artifacts and reduce radiation dose. Significant attention of image quality and computational implementation. Since has been devoted to optimizing computational performance then, many efforts have been made to extend the FDK algo- and to balancing conflicting requirements. Both theoretically rithm to other scanning configurations, leading to a series oriented and application-specific issues are also being ad- of FDK-like algorithms. In this special issue, Yan et al. pro- dressed. As a snapshot of the dynamically changing field of pose an approximate FDK-like reconstruction algorithm for CT, this special issue includes 10 high-quality original papers. tilted-gantry CT imaging [6]. The method improves the im- Because spiral cone-beam CT can be used for rapid vol- age reconstruction by filtering the projection data along a di- umetric imaging with high longitudinal resolution, the de- rection that is determined by CT parameters and the tilted- velopment of exact and efficient algorithms for image recon- gantry angle. Based on the idea that there is less redundancy struction from spiral cone-beam projection data has been a for the projection data away from the central scanning plane, subjectofactiveresearchinrecentyears.Katsevich’sfiltered Yang and Ning develop a heuristic cone-beam geometric de- backprojection (FBP) formula represents a significant break- pendent weighting scheme [7], which leads to a new FDK- through in this field [1]. In this special issue, Yang et al. pro- like half-scan algorithm. For correcting cone-beam artifacts pose a parallel implementation of Katsevich’s FBP formula in off-centered geometry, Valton et al. compare and evalu- [2] by the one-beam cover method, in which the backprojec- ate four different reconstruction methods [8], which are the tion procedure is independently driven by cone-beam pro- Alpha-FDK algorithm, a shift-invariant FBP method derived jections. Based on Katsevich’s work, generalized backprojec- from the T-FDK, an FBP method based on the Grangeat for- tion filtration (BPF) and FBP algorithms are developed to mula, and an iterative algebraic method. Tang et al. extend reconstructimagesfromdatacollectedalongmoreflexible the 3D weighted helical CB-FBP algorithm to handle helical scanning trajectories [3]. Using these recently developed al- pitches that are lower than 1 : 1 [9]. For helical over-scan, the gorithms, Yu et al. propose a local region reconstruction extended 3D weighted helical CB-FBP algorithm can signif- scheme [4]. The principal idea is to deliver a normal radia- icantly improve noise characteristics or dose efficiency com- tion dose to a local region of interest (ROI) that may contain pared to the original algorithm, while other advantages of a lesion while applying a very low radiation dose to the struc- the original algorithm, such as reconstruction accuracy and tures outside the ROI. Both the FBP and BPF algorithms can computational efficiency, can be maintained. produce excellent results with a minimal increment to the In addition to the exact and approximate CBCT algo- dose needed for purely local CT. rithms, iterative algorithms are important technologies in Despite important advancements in the development of medical X-ray CT. It is well known that a major weak- exact cone-beam reconstruction, approximate algorithms re- ness of the noniterative algorithms, either exact or approx- main practically and theoretically valuable. Feldkamp et al. imate, is that projection data are implicitly assumed to be 2 International Journal of Biomedical Imaging noise-free. However, noise is an inherent aspect of projec- Journal of Biomedical Imaging, vol. 2006, Article ID 17463, pp. tion data, especially for low-dose scans. Iterative algorithms 8 pages, 2006. are well suited to deal with image artifacts caused by pho- [3] S. Zhao, H. Yu, and G. Wang, “A unified framework for exact ton noise or other physical effects. Qi compares maximum a cone-beam reconstruction formulas,” Medical Physics, vol. 32, posteriori (MAP) reconstructions with Gaussian and non- no. 6, pp. 1712–1721, 2005. Gaussian priors [10]. After evaluating three representative [4] H. Yu, Y. Ye, S. Zhao, and G. Wang, “Local ROI reconstruction priors: the Gaussian prior, the Huber prior, and the Geman- via generalized FBP and BPF algorithms along more flexible McClure prior, Qi concludes that the Gaussian prior is as ef- curves,” International Journal of Biomedical Imaging, vol. 2006, Article ID 14989, pp. 7 pages, 2006. fective as the more