title: The X-ray transform projection of 3D mother wavelet function.
abstract: 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.
authors.affiliation: College of Mathematics and Econometrics, Hunan University, Hunan 410082, China.
authors.forename: Xiangyu
authors.initials: X
authors.lastname: Yang
authors.affiliation: ICT Research Center, Key Laboratory of Optoelectronic Technology and System of the Education Ministry of China, Chongqing University, Chongqing 400044, China ; College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China.
authors.forename: Jiqiang
authors.initials: J
authors.lastname: Guo
authors.affiliation: ICT Research Center, Key Laboratory of Optoelectronic Technology and System of the Education Ministry of China, Chongqing University, Chongqing 400044, China ; College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China.
authors.forename: Li
authors.initials: L
authors.lastname: Lu
authors.affiliation: ICT Research Center, Key Laboratory of Optoelectronic Technology and System of the Education Ministry of China, Chongqing University, Chongqing 400044, China ; College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China.
authors.forename: Li
authors.initials: L
authors.lastname: Zeng
mesh_terms: D000465:Algorithms; D005583:Fourier Analysis; D006801:Humans; D007091:Image Processing, Computer-Assisted; D021621:Imaging, Three-Dimensional; D008962:Models, Theoretical; D016011:Normal Distribution; D011856:Radiographic Image Enhancement; D011857:Radiographic Image Interpretation, Computer-Assisted; D012984:Software; D014057:Tomography, X-Ray Computed