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      FDK-Type Algorithms with No Backprojection Weight for Circular and Helical Scan CT

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      * ,
      International Journal of Biomedical Imaging
      Hindawi Publishing Corporation

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          Abstract

          We develop two Feldkamp-type reconstruction algorithms with no backprojection weight for circular and helical trajectory with planar detector geometry. Advances in solid-state electronic detector technologies lend importance to CT systems with the equispaced linear array, the planar (flat panel) detectors, and the corresponding algorithms. We derive two exact Hilbert filtered backprojection (FBP) reconstruction algorithms with no backprojection weight for 2D fan-beam equispace linear array detector geometry (complement of the equi-angular curved array detector). Based on these algorithms, the Feldkamp-type algorithms with no backprojection weight for 3D reconstruction are developed using the standard heuristic extension of the divergent beam FBP algorithm. The simulation results show that the axial intensity drop in the reconstructed image using the FDK algorithms with no backprojection weight with circular trajectory is similar to that obtained by using Hu's and T-FDK, algorithms. Further, we present efficient algorithms to reduce the axial intensity drop encountered in the standard FDK reconstructions in circular cone-beam CT. The proposed algorithms consist of mainly two steps: reconstruction of the object using FDK algorithm with no backprojection weight and estimation of the missing term. The efficient algorithms are compared with the FDK algorithm, Hu's algorithm, T-FDK, and Zhu et al.'s algorithm in terms of axial intensity drop and noise. Simulation shows that the efficient algorithms give similar performance in axial intensity drop as that of Zhu et al.'s algorithm while one of the efficient algorithms outperforms Zhu et al.'s algorithm in terms of computational complexity.

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          Most cited references31

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          An Inversion Formula for Cone-Beam Reconstruction

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            A general cone-beam reconstruction algorithm.

            Considering the characteristics of the X-ray microscope system being developed at SUNY at Buffalo and the limitations of available cone-beam reconstruction algorithms, a general cone-beam reconstruction algorithm and several special versions of it are proposed and validated by simulation. The cone-beam algorithm allows various scanning loci, handles reconstruction of rod-shaped specimens which are common in practice, and facilitates near real-time reconstruction by providing the same computational efficiency and parallelism as L.A. Feldkamp et al.'s (1984) algorithm. Although the present cone-beam algorithm is not exact, it consistently gives satisfactory reconstructed images. Furthermore, it has several nice properties if the scanning locus meets some conditions. First, reconstruction within a midplane is exact using a planar scanning locus. Second, the vertical integral of a reconstructed image is equal to that of the actual image. Third, reconstruction is exact if an actual image is independent of rotation axis coordinate z. Also, the general algorithm can uniformize and reduce z-axis artifacts, if a helix-like scanning locus is used.
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              Image reconstruction from cone-beam projections: necessary and sufficient conditions and reconstruction methods.

              Previously unknown sufficient conditions, a necessary condition, and reconstruction methods for image reconstruction from cone-beam projections are developed. A sufficient condition developed is contained in the following statement. Statement 5: If one every plane that intersects the object, there exists at least one cone-beam source point, then the object can be reconstructed. Reconstruction methods for an arbitrary configuration of source points that satisfy Statement 5 are derived. By requiring additional conditions on the configuration of source points, a more efficient reconstruction method is developed. It is shown that when the configuration of source points is a circle, Statement 5 is not satisfied. In spite of this, several suggestions are made for reconstruction from a circle of source points.
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                Author and article information

                Journal
                Int J Biomed Imaging
                IJBI
                International Journal of Biomedical Imaging
                Hindawi Publishing Corporation
                1687-4188
                1687-4196
                2012
                16 February 2012
                : 2012
                : 969432
                Affiliations
                Department of Electrical Engineering, Indian Institute of Science, Bangalore 560 012, India
                Author notes
                *A. V. Narasimhadhan: adhan@ 123456ee.iisc.ernet.in

                Academic Editor: Erik L. Ritman

                Article
                10.1155/2012/969432
                3296957
                22481912
                71bbab21-3dd4-4e14-905d-308dd78c87fd
                Copyright © 2012 A. V. Narasimhadhan and K. Rajgopal.

                This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

                History
                : 5 August 2011
                : 2 November 2011
                : 3 November 2011
                Categories
                Research Article

                Radiology & Imaging
                Radiology & Imaging

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