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The X-Ray Transform Projection of 3D Mother Wavelet Function

As we all know, any practical computed tomography (CT) projection data more or less contains noises. Hence, it will be inconvenient for the postprocessing of a reconstructed 3D image even when the noise in the projection data is white. The reason is that the noise in the reconstructed image may be n...

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Detalles Bibliográficos
Autores principales: Yang, Xiangyu, Guo, Jiqiang, Lu, Li, Zeng, Li
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2013
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3860119/
https://www.ncbi.nlm.nih.gov/pubmed/24376470
http://dx.doi.org/10.1155/2013/754829
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author Yang, Xiangyu
Guo, Jiqiang
Lu, Li
Zeng, Li
author_facet Yang, Xiangyu
Guo, Jiqiang
Lu, Li
Zeng, Li
author_sort Yang, Xiangyu
collection PubMed
description As we all know, any practical computed tomography (CT) projection data more or less contains noises. Hence, it will be inconvenient for the postprocessing of a reconstructed 3D image even when the noise in the projection data is white. The reason is that the noise in the reconstructed image may be nonwhite. X-ray transform can be applied to the three dimensional (3D) CT, depicting the relationship between material density and ray projection. In this paper, nontensor product relationship between the two dimensional (2D) mother wavelet and 3D mother wavelet is obtained by taking X-ray transform projection of 3D mother wavelet. We proved that the projection of the 3D mother wavelet is a 2D mother wavelet if the 3D mother wavelet satisfies certain conditions. So, the 3D wavelet transform of a 3D image can be implemented by the 2D wavelet transform of its X-ray transform projection and it will contribute to the reduction complexity and computation time during image processing. What is more, it can also avoid noise transfer and amplification during the processing of CT image reconstruction.
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spelling pubmed-38601192013-12-29 The X-Ray Transform Projection of 3D Mother Wavelet Function Yang, Xiangyu Guo, Jiqiang Lu, Li Zeng, Li Comput Math Methods Med Research Article As we all know, any practical computed tomography (CT) projection data more or less contains noises. Hence, it will be inconvenient for the postprocessing of a reconstructed 3D image even when the noise in the projection data is white. The reason is that the noise in the reconstructed image may be nonwhite. X-ray transform can be applied to the three dimensional (3D) CT, depicting the relationship between material density and ray projection. In this paper, nontensor product relationship between the two dimensional (2D) mother wavelet and 3D mother wavelet is obtained by taking X-ray transform projection of 3D mother wavelet. We proved that the projection of the 3D mother wavelet is a 2D mother wavelet if the 3D mother wavelet satisfies certain conditions. So, the 3D wavelet transform of a 3D image can be implemented by the 2D wavelet transform of its X-ray transform projection and it will contribute to the reduction complexity and computation time during image processing. What is more, it can also avoid noise transfer and amplification during the processing of CT image reconstruction. Hindawi Publishing Corporation 2013 2013-11-27 /pmc/articles/PMC3860119/ /pubmed/24376470 http://dx.doi.org/10.1155/2013/754829 Text en Copyright © 2013 Xiangyu Yang et al. https://creativecommons.org/licenses/by/3.0/ 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.
spellingShingle Research Article
Yang, Xiangyu
Guo, Jiqiang
Lu, Li
Zeng, Li
The X-Ray Transform Projection of 3D Mother Wavelet Function
title The X-Ray Transform Projection of 3D Mother Wavelet Function
title_full The X-Ray Transform Projection of 3D Mother Wavelet Function
title_fullStr The X-Ray Transform Projection of 3D Mother Wavelet Function
title_full_unstemmed The X-Ray Transform Projection of 3D Mother Wavelet Function
title_short The X-Ray Transform Projection of 3D Mother Wavelet Function
title_sort x-ray transform projection of 3d mother wavelet function
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3860119/
https://www.ncbi.nlm.nih.gov/pubmed/24376470
http://dx.doi.org/10.1155/2013/754829
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