Computer Science and Application
Vol.4 No.10(2014), Article ID:14247,7 pages
DOI:10.12677/CSA.2014.410033

CT Image Reconstruction Algorithm Based on Anisotropic Total Variation Minimization

Ying Zhang, Dan Wang

College of Computer Science, Beijing University of Technology, Beijing

Email: 983956323@qq.com

Received: Sep. 4th, 2014; revised: Oct. 4th, 2014; accepted: Oct. 15th, 2014

ABSTRACT

In many practical applications, due to the data acquisition time, dose, and geometric constraint scanning, only in a limited Angle range, various data is available to acquire. It is the so-called few-view problem. In recent years, the Total Variation (TV) minimization model, using alternating direction method (ADM) in sparse optimization algorithm shows better reconstruction results among these TV-based algorithms. However, Isotropic TV minimization based algorithms for fewview reconstruction has not so good accuracy and there is further improvement to achieve. Aiming at this problem, Anisotropic TV minimization algorithm is proposed in this paper. The algorithm is based on ADM and uses sparse optimization theory. Experimental results demonstrate that the proposed method compared with Isotropic TV minimization algorithm, has higher reconstruction accuracy and a more excellent comprehensive performance.

Keywords:CT Image Reconstruction, Few-View Reconstruction, Total Variation Minimization, Alternating Direction Method, Anisotropic Total Variation Minimization

CT图像重建算法

Email: 983956323@qq.com

1. 引言

2. 基于各向异性TV最小化算法的设计与实现

2.1. 压缩感知理论下的图像稀疏表示

2006年Donoho[3] ，Candes和Tao[2] [4] 共同提出了CS理论，近年来在压缩图像、医学图像、数模转换、雷达成像、天文学、通信等领域都得到应用[10] 。相对于传统的从频域中获取数据重构图像的方法，CS理论有着不同的性质，即只需要通过少量的样本点就能够精确地重构原来的图像[11] 。

CS理论的基本结论为：对一个稀疏的离散信号，只需知道这个信号的部分频域取值，就能以高概率精确恢复这一信号。具体的恢复方式是通过求解一个凸规划实现的，该规划的目标函数为此信号的l1范数最小，约束条件由已知的频域取值得到。具体形式表示为如(1)所示。

(1)

(2)

(3)

2.2. 基于各向异性TV最小化算法的设计与实现

(4)

(a) 体模                     (b) DCT                 (c) DWT                   (d) TV

Figure 1. Schematic diagram of sparse transformed

(5)

(6)

(7)

(8)

(9)

3. 实验结果

3.1. 稀疏性及采样条件分析

3.2. 仿真数据重建

Table 1. Simulation experiments scanning and reconstruction parameters

(a)(b)

Figure 2. 10 angle reconstruction results (a) the results of the isotropic TV reconstruction algorithm; (b) the results of the anisotropic TV reconstruction algorithm

Table 2. RMSE of reconstruction results at different angles

4. 结论

(a)(b)

Figure 3. 12 angle reconstruction results (a) the results of the isotropic TV reconstruction algorithm; (b) the results of the anisotropic TV reconstruction algorithm

(a)(b)

Figure 4. 14 angle reconstruction results (a) the results of the isotropic TV reconstruction algorithm; (b) the results of the anisotropic TV reconstruction algorithm

(a)(b)

Figure 5. 16 angle reconstruction results (a) the results of the isotropic TV reconstruction algorithm; (b) the results of the anisotropic TV reconstruction algorithm

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