小波分析论文

384IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 28, NO. 3, MARCH 2009A Filtered Backprojection Algorithm for Triple-Source Helical Cone-Beam CTJun Zhao*, Member, IEEE, Yannan Jin, Yang Lu, and Ge Wang, Fellow, IEEEAbstract—Multisource cone-beam computed tomography (CT) is an attractive approach of choice for superior temporal resolution, which is critically important for cardiac imaging and contrast enhanced studies. In this paper, we present a ltered-backprojection (FBP) algorithm for triple-source helical cone-beam CT. The algorithm is both exact and efcient. It utilizes data from three inter-helix PI-arcs associated with the inter-helix PI-lines and the minimum detection windows dened for the triple-source conguration. The proof of the formula is based on the geometric relations specic to triple-source helical cone-beam scanning. Simulation results demonstrate the validity of the reconstruction algorithm. This algorithm is also extended to a multisource version for (2 + 1)-source helical cone-beam CT. With parallel computing, the proposed FBP algorithms can be signicantly faster than our previously published multisource backprojection-ltration algorithms. Thus, the FBP algorithms are promising in applications of triple-source helical cone-beam CT. Index Terms—Computed tomography (CT), cone-beam, lteredbackprojection (FBP), helical scanning, triple-source.I. INTRODUCTION HE recently introduced Siemens’ dual-source computed tomography (CT) allows much-improved temporal resolution, and has received a major attention in the medical imaging eld. A natural extension of the dual-source system is a triplesource cone-beam CT (CBCT) scanner for even better temporal resolution at an additional system cost. As a follow-up to our previously published work on backprojection-ltration (BPF) based triple-source CBCT, this paper presents an exact lteredbackprojection (FBP) algorithm for triple-source helical CBCT, which can be implemented using parallel-computing techniques much more efciently than the BPF counterpart. Many exact and efcient methods were developed for spiral/helical cone-beam CT over past years [1]–[15]. The focus loci range from specic to more general, and fromManuscript received June 04, 2008; revised August 01, 2008. First published August 26, 2008; current version published February 25, 2009. This work was supported in part by National Science Foundation of China under Grant 30570511 and Grant 30770589, and in part by the National Institutes of Health/National Institute of Biomedical Imaging and Bioengineering (NIH/NIBIB) under Grant EB002667 and Grant EB004287. Asterisk indicates corresponding author. *J. Zhao is with the Department of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China (e-mail: junzhao@). Y. Jin and Y. Lu are with the Department of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China (e-mail: yannanjin@; lvyang@ ). G. Wang is with the Biomedical Imaging Division, Virginia Tech/Wake Forest University (VT-WFU) School of Biomedical Engineering and Science, Virginia Tech, Blacksburg, VA 24061 USA (e-mail: wangg@vt.edu ). Color versions of one or more of the gures in this paper are available online at . Digital Object Identier 10.1109/TMI.2008.2004817Tsingle-source scanning to multisource congurations. In 2002, Katsevich introduced an exact ltered-backprojection (FBP) algorithm [1]. Then, Zou and Pan presented an exact backprojection-ltration (BPF) algorithm [2]. These algorithms utilize projection data from a PI-arc based on the so-called PI-line [16] and Tam–Danielsson window [16], [17]. The Katsevich FBP algorithm uses a 1-D Hilbert transform of derivatives of differential projection data within a window slightly larger than the Tam–Danielsson window. The merit of the Zou–Pan’s BPF formula is that it uses only the data in the Tam–Danielsson window and accommodates certain types of transverse data truncation. To extend these results to the case of general scanning trajectories, Katsevich also presented a general scheme for constructing inversion algorithms [3]. Ye et al. [4], [5] proved the validity of the BPF formula in the case of a general scanning curve and derived a general Katsevich-type FBP formula [6]. Pack et al. [7], [8] also introduced the BPF and FBP formulas that can deal with discontinuous source curves. Other independent algorithms on general CBCT were also reported [46], [47]. Chen [9] gave an alternative derivation of the Katsvich conebeam reconstruction formula based on the Tuy inversion formula [18]. Also, based on the Tuy formula, Zhao, Yu and Wang [10], [11] unied the above FBP and BPF formulas using appropriate operators. Cardiac imaging and contrast enhanced studies are very important medical CT applications. Rapid data collection and exact reconstruction are highly desirable in the clinical settings. One approach to improve CT temporal resolution is to apply a half-scan technique [19]–[21]. However, further reduction of the source angular range is not generally possible since the data sufciency condition [18] cannot be satised by a dataset less than a half-scan. Another approach is to use a multisource system [21]–[27], [12]–[15]. Theoretically, higher temporal resolution can be achieved as the number of sources becomes larger. The initial experience with the commercial dual-source CT system has been very encouraging in cardiac imaging and coronary angiography, which show that the dual-source CT generates high quality images with ultra high temporal resolution, making functional evaluation of the heart valves and myocardium clinically possible [23]–[26]. Unlike previous multisource systems that use either a circle scanning locus or an approximate reconstruction algorithm [21], [22], for the rst time we recently proposed a generic design for exact triple-source helical CBCT [12]–[15]. Such an exact BPF reconstruction algorithm for triple-source helical CBCT [14], [15] was developed based on the Zhao window [12], [13] and the inter-helix PI-lines [12], [13]. The Zhao window is the minimum detection window for triple-source helical CBCT, which is a0278-0062/$25.00 2009 IEEEAuthorized licensed use limited to: IEEE Xplore. Downloaded on March 9, 2009 at 03:06 from IEEE Xplore. Restrictions apply.