﻿ CT系统模型新模板设计的发现 A Discovery of New Template Design of CT System Model

Computer Science and Application
Vol.08 No.04(2018), Article ID:24530,7 pages
10.12677/CSA.2018.84055

A Discovery of New Template Design of CT System Model

Xuanlin Chen1, Tao Luo1, Huiling He1, Fang Wang1,2*

1College of Science, Hunan Agricultural University, Changsha Hunan

2Agricultural Mathematical Model and Data Process Center, Hunan Agricultural University, Changsha Hunan

Received: Apr. 4th, 2018; accepted: Apr. 19th, 2018; published: Apr. 26th, 2018

ABSTRACT

Computed Tomography (CT) technology has been widely used in the field of medicine and engineering. The shape of the template is crucial to the calibration of CT system parameters. In this paper, the ordinary single ellipse and small circle template are improved. We design three new templates. The receiving information is obtained by Radon transform and R-L filter firstly, and then their reconstruction images are acquired based on convolution back projection reconstruction algorithm. Furthermore, we make a quantitative assessment of the reconstruction effect by the sensitivity, specificity and Youden index. In addition, in order to investigate the anti-noise, the original template and the new templates are added to the Gauss noise of different strength, respectively. The experimental result shows that the new templates have better noise resistance than the original template. An interesting finding is that the template generated by geometric figure of a single reference frame with polygon outline is better than the template produced by multi reference frame geometry with the arc line for the reconstruction of CT.

Keywords:Polygon Template, Computed Tomography (CT), Convolution, R-L Filtering, Youden Index

CT系统模型新模板设计的发现

1湖南农业大学理学院，湖南 长沙

2湖南农业大学农业数学建模与数据处理中心，湖南 长沙

1. 引言

2. 数据来源和模型假设

3. 卷积反投影重构图像

${h}_{R-L}\left(nd\right)=\left\{\begin{array}{ll}1/\left(4{d}^{2}\right)\hfill & n=0;\hfill \\ 0\hfill & n为偶数;\hfill \\ -1/\left({n}^{2}{\text{π}}^{2}{d}^{2}\right)\hfill & n为奇数.\hfill \end{array}$ (1)

$\begin{array}{c}\stackrel{˜}{p}\left(n,m\right)=p\left(n,m\right)×h\left(n\right)\\ =\underset{l=-{N}_{i}}{\overset{{N}_{i}}{\sum }}p\left(n-l,m\right)h\left(l\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}n=0,1,2,\cdots ,255\end{array}$ (2)

$\begin{array}{c}\stackrel{˜}{p}\left({n}_{0}+\delta \right)=\stackrel{˜}{p}\left({n}_{0}\right)+\delta \left[\stackrel{˜}{p}\left({n}_{0}+1\right)-\stackrel{˜}{p}\left({n}_{0}\right)\right]\\ =\left(1-\delta \right)\stackrel{˜}{p}\left({n}_{0}\right)+\delta \stackrel{˜}{p}\left({n}_{0}+1\right)\end{array}$ (3)

$\begin{array}{c}{x}_{r}={x}_{i}\mathrm{cos}\theta +{y}_{j}\mathrm{sin}\theta \\ =\left(i-\frac{N+1}{2}\right)\mathrm{cos}\theta +\left(j-\frac{N+1}{2}\right)\mathrm{sin}\theta \end{array}$ (4)

${\stackrel{˜}{x}}_{r}={x}_{r}+\frac{N-1}{2}$ ，则射束运算如下：

${\stackrel{˜}{x}}_{r}={C}_{\theta }+\left(i-1\right)\mathrm{cos}\theta +\left(j-1\right)\mathrm{sin}\theta =整数\left({n}_{0}\right)+小数\left(\delta \right)$ (5)

$\stackrel{˜}{x}|{}_{\theta =m\Delta }={\stackrel{˜}{x}}_{r,m}\left(i,j\right)=\left(i-1\right)\mathrm{cos}m\Delta +\left(j-1\right)\mathrm{sin}\left(m\Delta \right)+{C}_{m}.$ (6)

${a}_{m}\left(i,j\right)={a}_{m-1}\left(i,j\right)+\stackrel{˜}{p}\left[{\stackrel{˜}{x}}_{r,m}\left(i,j\right),m\Delta \right],\text{\hspace{0.17em}}\text{\hspace{0.17em}}m=1,2,\cdots ,180.$ (7)

$m=180$ 时，图像重建完毕。卷积反投影重建流程图 [8] 如下。

4. 基于不同滤波器下新模板的构建与对比

Figure 1. Template map of the original data

$\left\{\begin{array}{l}Se=1-\frac{1}{size\left({I}_{1}^{\left(k\right)}\right)}\underset{\left(i,j\right)\in {I}_{1}^{\left(k\right)}}{\sum }|{I}^{\left(k\right)}\left(i,j\right)-{J}^{\left(k\right)}\left(i,j\right)|,\hfill \\ Sp=1-\frac{1}{size\left({I}_{0}^{\left(k\right)}\right)}\underset{\left(i,j\right)\in {I}_{0}^{\left(k\right)}}{\sum }|{I}^{\left(k\right)}\left(i,j\right)-{J}^{\left(k\right)}\left(i,j\right)|\hfill \\ Youden=Se+Sp-1.\hfill \end{array},$ (8)

Figure 2. Reconstruction flow chart based on convolution back projection

Figure 3. Reception information and reconstruction effect of new templates. The first column is absorptivity matrix gray image; the second column is receiving information gray image; and the third column is the reconstructed image

Table 1. Reconstruction effect of original template and three new templates

5. 结语

Table 2. Youden index of reconstruction effect of original template and new templates under different noise intensity

Figure 4. Reconstruction effect diagram of original template and new templates under different noise intensity

Figure 5. The change rate of Youden index of original template and the three new templates with increasing noise intensity

A Discovery of New Template Design of CT System Model[J]. 计算机科学与应用, 2018, 08(04): 496-502. https://doi.org/10.12677/CSA.2018.84055

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16. NOTES

*通讯作者。