小波分析论文

392IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 28, NO. 3, MARCH 2009Fig. 9. Zhao Windows cone-beam projected onto the detector plane for triple-source (a) and quintuple-source (b). The region bounded by the dark solid lines is Zhao Window. The region bounded by the dark dashed lines is Tam–Danielsson Window. The light dotted lines are the other two helices. u v is the coordinate system on the detector plane.0andwith as the vertex, . The symbol is the angular parameter indicating the source position . Fig. 8(b) shows the Zhao Window for the source position in the quintuple-source case. Fig. 9(b) shows the Zhao Window cone-beam projected onto the detector plane for quintuple-source. APPENDIX III Scattering Reduction: One concern with triple-source CT is that the improvement in temporal resolution may be offset by the increment in scattering artifacts. In fact, there were similar arguments against the dual-source system in comparison with the single-source counterpart prior to the introduction of the Siemens Denition dual-source CT scanner. Actually, the Siemens dual-source CT scanner has received a very positive market response, which is encouraging for our proposed triplesource extension. Philosophically, we do not believe that the source and detector technology will not be advanced to accommodate the triple source system sooner or later. The Siemens dual-source CT has been claimed to have a dose benet because the second detector is smaller, and the dose is reduced at the edge of the eld-of-view. The dual-source CT scanner can deliver double the power but it needs only half the dose for cardiac applications—without any compromise in image quality [51]. It has been reported that cross scatter is smaller with the decreased collimation -width or the decreased object size for dual-source CT [52]. These guidelines should be valuable for optimization of triple-source CT. Furthermore, we underline that the height of the Zhao window for triple-source CT is of only one third of theTam–Danielsson window (please refer to Fig. 8(a) and Fig. 9(a) in Appendix II). Theoretically, the total dose delivered to the object remains the same as in the single-source case. For each source-detector pair of the triple source system, we have a signicantly smaller collimation in -width, and the cross scattering effect should be proportionally smaller. In practice, to decrease cross scattering and improve temporal resolution, low or mediate pitch triple-source CT scanning may well be an optimal balance. Another potential strategy is to utilize shutters so that at any time instant the object is only exposed to one or two sources, since the shutters can be rapidly opened or closed in an alternative fashion [53]. Other scattering correction methods may also be used for the same purpose, such as the recently developed interior reconstruction techniques which have allowed exact reconstruction from purely local data assuming knowledge on a subregion in the volume of interest [50]. These promising techniques may be adapted for triple source CT to improve temporal resolution signicantly at an acceptable radiation dose level. ACKNOWLEDGMENT The authors would like to thank the anonymous reviewers for their comments and suggestions. REFERENCES[1] A. Katsevich, “An improved exact ltered backprojection algorithm for spiral computed tomography,” Adv. Appl. Math., vol. 32, pp. 681–697, 2004. [2] Y. Zou and X. Pan, “Exact image reconstruction on PI-lines from minimum data in helical cone-beam CT,” Phys. Med. Biol., vol. 49, pp. 941–959, 2004. [3] A. Katsevich, “A general scheme for constructing inversion algorithms for cone beam CT,” Int. J. Math. Math. Sci., vol. 21, pp. 1305–1321, 2003. [4] Y. B. Ye, S. Y. Zhao, H. Y. Yu, and G. Wang, “Exact reconstruction for cone-beam scanning along nonstandard spirals and other curves,” in Proc. SPIE, Aug. 2004, vol. 5535, pp. 293–300. [5] Y. Ye, S. Zhao, H. Yu, and G. Wang, “A general exact reconstruction for cone-beam CT via backprojection-ltration,” IEEE Trans. Med. Imag., vol. 24, no. 9, pp. 1190–1198, Sep. 2005. [6] Y. Ye and G. Wang, “Filtered backprojection formula for exact image reconstruction from cone-beam data along a general scanning curve,” Med. Phys., vol. 30, pp. 42–48, 2005.Authorized licensed use limited to: IEEE Xplore. Downloaded on March 9, 2009 at 03:06 from IEEE Xplore. Restrictions apply.