Research on tomographic image reconstruction algorithms based on fixed-point rotation X-CT system
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Research on tomographic image reconstruction algorithms based on fixed-point rotation X-CT system Chao Ding 1,2 & Weiwei Wang 1 & Hailang He 1 & Wanting Yang 1 Received: 8 July 2019 / Revised: 3 March 2020 / Accepted: 17 March 2020 # Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract
Aiming at the problem of parameter calibration and image reconstruction of typical twodimensional CT system, this paper uses back projection, iradon function, Fourier transform, Lambert law, visualization and other methods to establish projection centroid model, convolution back projection model, TV constrained iterative filtering back projection model, and uses MATLAB, Solidworks, Lingo and other software to visualize data types, so as to achieve better results. Better to find X-CT system tomography reconstruction methods. Keywords Lambert law . TV constrained iterative FBP model . Central slice theorem . Passive ray drive
1 Questions raised CT scanning can obtain the structural information of biological tissues and engineering materials by using the absorption characteristics of radiation energy without destroying the samples. A typical two-dimensional CT system is shown in Fig. 1. Parallel X-rays are perpendicular to the detector plane. Each detector unit is considered as a receiving point, and is arranged equidistantly [3, 6, 7]. The relative position of X-ray emitter and detector is fixed, and the whole transmitting-receiving system rotates counter-clockwise 180 times around a fixed rotating center. A calibration template consisting of two uniform solid media is placed on a square tray. The geometric information of the template is shown in Fig. 2. The value of each point reflects the absorption intensity of the point, which is called “absorptivity”. Based on the template and the received information, the position of the rotating center of the CT system in the square tray, the distance between detector units and 180.
* Chao Ding [email protected]
1
College of Environment and Energy Engineering, Anhui Jianzhu University, Hefei 230031 Anhui, China
2
State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei 230026, People’s Republic of China
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Fig. 1 Schematic diagram of CT system
Fig. 2 Template sketch (Unit: mm)
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2 Variables and symbolic description in mathematical modeling Table 1. Table 1 Variables and Symbolic Descriptions Serial number
Symbol
Symbolic Description
1 2 3 4 5 6 7 8 9 10 11 12
x f(x, y) d Pabs. p0 λ F(x, y) θ g(x, θ) T φ D
Abscissa of the center of rotation Reconstructed image coordinates by projection Unit spacing X-ray energy absorption Initial intensity of X-ray Medium absorptivity Fourier transform Incidence angle or line of sight direction When the incident angle is 0, the pixel value X-ray transmittance Light deflection angle Pixel density
3 Establishment and solution of mathematical model 3.1 Fixed-point rotation model based on template particle 3.1.1 Determin
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