c154-FDK-TS-SCT(5)

小波分析论文

388IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 28, NO. 3, MARCH 2009TABLE I PARAMETERS USED IN THE SIMULATIONFig. 3. Detector plane and coordinate system for the triple-source FBP CBCT based on an inter-helix PI-line. x y z is the 3-D xed-coordinate system, d d d the 3-D rotated coordinate system for the source a (t), x the 1-D coordinate system for the inter-helix PI-line a a , and u v the 2-D coordinate system on the corresponding detector plane of a (t). The actual direction of the Hilbert ltering is along the cone-beam projection of a a on the detector plane, shown as the dashed–dotted line.000 00a complicated rebining procedure is needed to convert the reconstructed image from the inter-helix PI-line-associated system to the rectangular system. Clearly, the FBP scheme is two steps faster than the BPF counterpart, given sufcient computing resources. On the other hand, BPF algorithms have merits too. For example, BPF algorithms can support some transverse truncation in the projection data while FBP cannot. The recently developed interior reconstruction techniques have allowed exact reconstruction from purely local data assuming knowledge on a subregion in the volume of interest [30], [50], [54]. These promising techniques may be adapted for triple-source cardiac CT at much reduced radiation dose. Better scattering correction methods may also be used for the same purpose. Our proposed triple-source FBP algorithm has theoretical and practical values, because it is an intermediate step towards a spatially invariant FBP method like the Katsevich helical conebeam algorithm in the single source case [1], suits better for parallel computation, and also serves as the benchmark for development of approximate cone-beam algorithms in the triple-source case. Our ultimate goal is to develop exact and efcient FBP algorithms in the triple-source case. Because the FBP and BPF are quite different in the computational structure, in the identical imaging geometry separate papers are published on reconstruction methods in these formats; for example, BPF and FBP algorithms in the standard helical scanning case by Katsevich [1] and Pan’s group [2], [32], BPF and FBP algorithms in the general smooth curve scanning case by Wang’s group [5], [6]. We hope that this paper will be the rst one on the FBP algorithm in the triple-source case, and be followed by more papers towards optimal imaging performance and highest computationalFig. 4. Representative reconstruction results with the Shepp–Logan phantom in the inter-helix PI-line based coordinate system. (a) and (b) Reconstructed slices f (x ; t ; t ) in inter-helix PI-line based coordinates, where t was xed, and t and x formed the vertical and horizontal axes. Specically, t was varied from t + 0:88 to t + 1:12 , and x was from 12:5 cm to 12.5 cm. The two images were reconstructed at t = 0:5 and 0:375 , respectively. The display window is [0.99, 1.05]; (c) and (d) show the proles along the lines t = 0:5 in (a) and x = 1:66 cm in (b), respectively.00 0efciency. Actually, we recently developed a spatially invariant FBP method in the triple-source saddle scanning case [55]. III. SIMULATION RESULTS Let us consider the reconstruction on the inter-helix PI-line for a xed . The -axis is made along the inter-helix PI-line. Denote the object on the inter-helix PI-line as function at , where and are the angular parameters of and , respectively. The triple-source FBP algorithm can be implemented in the following steps.Authorized licensed use limited to: IEEE Xplore. Downloaded on March 9, 2009 at 03:06 from IEEE Xplore. Restrictions apply.