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ALGEBRAIC CORRECTION FOR METAL ARTIFACT REDUCTION IN COMPUTED TOMOGRAPHY

Journal of the Korean Society for Industrial and Applied Mathematics, v.18 no.2, 2014년, pp.157 - 166  

Jeon, Kiwan (Division of Computational Science in Mathematics, National Institute for Mathematical Science) ,  Kang, Sung-Ho (Division of Computational Science in Mathematics, National Institute for Mathematical Science) ,  Ahn, Chi Young (Division of Computational Science in Mathematics, National Institute for Mathematical Science) ,  Kim, Sungwhan (Division of Liberal Arts, Hanbat National University)

Abstract AI-Helper 아이콘AI-Helper

If there are metals located in the X-ray scanned object, a point outside the metals has its range of projection angle at which projections passing through the point are disturbed by the metals. Roughly speaking, this implies that attenuation information at the point is missing in the blocked project...

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AI 본문요약
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제안 방법

  • In this paper we propose a new MAR algorithm which is called the algebraic correction technique (ACT) using an interim image of the attenuation coefficient outside the metal region. The attenuation coefficient is usually calculated from the measured projection data by FBP and algebraic reconstruction technique(ART) basically proposed by Kaczmarz [19].
  • In this paper, we take a different approach to filling up the metal trace in the sinogram. Instead of using the boundary projections of the metal trace, we exploit an interim image of the attenuation coefficient reconstructed from incomplete projection data. Let M be the number of measured projection data for all projection angles and let p = (p1, p2, · · · , pM) ∈ # be the measured projection data.
  • Summary of the proposed method. Unlike the conventional inpainting methods to use the boundary data of the metal trace in the sinogram, the proposed ACT exploits an interim image of the attenuation coefficient as prior information for MAR. Briefly, the proposed method is based on the following steps:

이론/모형

  • To do so, we are forced to solve a linear system with the incomplete projection data. In this paper, in the purpose of avoiding possible computational cost in dealing with a large linear system, we generated a linear system defined on coarse grids and solved it using the Tikhonov regularized least squares method. However, there is not a study on design of a linear system and its inversion method to minimize computational cost and maximize image quality.
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참고문헌 (25)

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  7. Y. Chen, Y. Li, H. Guo, Y. Hu, L. Luo, X. Yin, J. Gu, and C. Toumoulin, CT Metal Artifact Reduction Method Based on Improved Image Segmentation and Sinogram In-Painting, Mathematical Problems in Engineering, 2012, Article ID 786281. 

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  9. E.Meyer, R. Raupach, M. Lell, B. Schmidt, and M. Kachelriess, Normalized metal artifact reduction (NMAR) in computed tomography, Med. Phys., 37 (2010), 5482-5493. 

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  17. M. Bertalmio, G. Sapiro, V. Caselles and C. Ballester, Image Inpainting, Proceedings of SIGGRAPH 2000, New Orleans, USA, July 2000. 

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  20. R. Gordon, R. Bender, and G.T. Herman, Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography, J. Theoret. Biol., 29 (1970), 471-482. 

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