小波分析论文

390IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 28, NO. 3, MARCH 2009Fig. 6. Representative reconstruction results with the Defrise phantom in the Cartesian coordinate system. (a) A reconstructed image of the Defrise disk phantom with the display window [0, 1]. Typical proles are shown along the lines specied by (b) x , and (c) x . and z and y at x= 0 cm= 0 cm= 0 cm= 0 cm= 0 cmwhere, , and . First, let us extend the concept of the Zhao windows into -source helical CB scanning. For the the case of , the corresponding Zhao window is the region source on the scanning cylinder bounded by the nearest helix turn and the nearest helix turn of of , . (The definition of Zhao window is given in the Appendix II). Then, and , , we have the inter-helix PI-line for , , that interat one point and at another point with the sects absolute difference of the angular parameter values at both the intersection points less than . The proofs of the existence and uniqueness properties of the inter-helix PI-lines are analogous to the proof of Theorem 2 in [12], [13]. Similarly, we have the sources backprojection operator forFig. 7. inter-helix PI-arcs (coarse solid curve-segments) a a , a a and a a for x.holds for all malization condition:, provided that the mapping ( ) satises the nor-(23) where , and , andIj(27) The normalization condition (27) holds for (24)Finally, let (25) then Theorem 3 can be extended to the following theorem for sources. -source FBP reconstruction formula] Theorem 3: [ Let be a standard helix in parameterized by a function (22), , and . Then, the inversion formula (28) Theorems 2 and 3 can also be extended to the cases of nonstandard helices in a similarly fashion. Clearly, the more sources are used, the better the temporal resolution can be achieved, but the higher the system cost will be needed. How to place multiple sources and detectors under the physical constraints is a major issue in the system development, especially when more than two sources are used. Given the focus of this paper on the algorithm development, we would like only to point out that X-ray sources would be made more compact, more powerful and more cost-effective in the future to(26)Authorized licensed use limited to: IEEE Xplore. Downloaded on March 9, 2009 at 03:06 from IEEE Xplore. Restrictions apply.