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Inventi Impact: X-Ray Optics & Instrumentation

Articles

  • Inventi:exoi/57/14
    THE X-RAY TRANSFORM PROJECTION OF 3D MOTHER WAVELET FUNCTION
    30-Jun-2014 Research 2014 : July - September
    Xiangyu Yang, Jiqiang Guo, Li Lu, Li Zeng

    Aswe all know, any practical computed tomography (CT) projection datamore or less contains noises.Hence, itwill be inconvenient\nfor the postprocessing of a reconstructed 3D image even when the noise in the projection data is white. The reason is that the\nnoise in the reconstructed image may be nonwhite. X-ray transform can be applied to the three dimensional (3D) CT, depicting\nthe relationship between material density and ray projection. In this paper, nontensor product relationship between the two\ndimensional (2D) mother wavelet and 3D mother wavelet is obtained by taking X-ray transform projection of 3D mother wavelet.\nWe proved that the projection of the 3Dmother wavelet is a 2Dmother wavelet if the 3Dmother wavelet satisfies certain conditions.\nSo, the 3D wavelet transformof a 3D image can be implemented by the 2D wavelet transformof its X-ray transformprojection and\nit will contribute to the reduction complexity and computation time during image processing.What is more, it can also avoid noise\ntransfer and amplification during the processing of CT image reconstruction.

    How to Cite this Article
    CC Compliant Citation: Xiangyu Yang, Jiqiang Guo, Li Lu, and Li\nZeng, â??The X-Ray Transform Projection of 3D Mother Wavelet\nFunction,â? Computational and Mathematical Methods in Medicine,\nvol. 2013, Article ID 754829, 9 pages, 2013.\ndoi:10.1155/2013/754829.\nCopyright © 2013 Xiangyu Yang et al. This article is distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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