小波分析论文

ZHAO et al.: A FILTERED BACKPROJECTION ALGORITHM FOR TRIPLE-SOURCE HELICAL CONE-BEAM CT391Fig. 8. Zhao Windows for the source position a (t ) in the triple-source case (a) and quintuple-source case (b). The region bounded by the coarse solid curved lines is the Zhao Window.facilitate prototyping of multisource systems, and will not discuss the related technical issues further. While we have concentrated on the development of exact triple-source helical CBCT algorithms, we recognize that approximate CBCT algorithms should not be overlooked. As Tang et al. pointed out [44], [45], approximate CBCT algorithms have important merits in practical applications. In reference to the classic and recent ndings on approximate CBCT [21]–[27], [39]–[45], the triple-source FBP algorithms presented in this paper may guide new development of approximate reconstruction algorithms for triple-source CBCT in both helical and circular scanning modes. In conclusion, we have reported a triple-source FBP algorithm for helical CBCT. Our results allow exact and efcient image reconstruction with ultra-high temporal resolution. With adequate parallel computing hardware, our proposed triple-source FBP approach would run much faster than the BPF counterpart. Therefore, the triple-source FBP algorithm should be a good choice for practical helical CBCT. Our simulation results have veried our formulation, demonstrating excellent image quality. Finally, we have extended our work -source helical CBCT to inspire or into the case of facilitate development of CT and micro-CT systems along this multi-source direction.For instance, if the three X-ray sources are symmetrically arranged, the three helices would be equally spaced. Thus the phases of the helices are (30) Then, for the inter-helix PI-line between and rotation angles at the intersection points should satisfy , the(31) The inter-helix PI-lines for -source can be dened in the same way. As shown in Fig. 7, in the triple-source case there are three , and for . The correinter-helix PI-lines sponding inter-helix PI-arcs are the coarse solid curve-segments , and . APPENDIX II A) Denition of Zhao Window for Triple-Source: Dene Zhao Window as the region of the scanning cylinder surface that is bounded by the helix turns and with as the vertex, . The symbol is the . angular parameter indicating the source position Fig. 8(a) shows the Zhao Window for the source position in the triple-source case. Fig. 9(a) shows the Zhao Window cone-beam projected onto the detector plane for triple-source. It is assumed that the detector plane is parallel to the axis of the spiral and is tangent to the spiral cylinder at the point opposite to the source. -Source: B) Denition of the Zhao Window for Dene Zhao Window as the region of the scanning cylinder surface that is bounded by the helix turnsAPPENDIX I Inter-Helix PI-Lines and Inter-Helix PI-Arcs: The denition of inter-helix PI-lines for the triple-source case is as follows: . is dened by Denition: Let and can (21). The inter-helix PI-line between helices be dened as a line such that and , 1) The line intersects the two helices at respectively; 2) The rotation angles and corresponding to the two intersections satisfy the following condition(29)Authorized licensed use limited to: IEEE Xplore. Downloaded on March 9, 2009 at 03:06 from IEEE Xplore. Restrictions apply.