一种去除CT图像中同心椭圆伪影的变分模型

栗乔新; 金科; 庞志峰

doi:10.15953/j.ctta.2022.085

一种去除CT图像中同心椭圆伪影的变分模型

栗乔新^a,,
金科^b,
庞志峰^a, ,

1.
数学与统计学院；河南大学
2.
计算机与信息工程学院，河南开封475000 河南大学

基金项目: 国家自然科学基金（图像处理问题中的两类曲率正则化方法及应用（12071345））；河南省科技厅重点研发与推广专项（核磁共振影像（MRI）重建与分割中的数学理论及其高效数值方法研究（212102210511））。

详细信息

作者简介:
栗乔新: 男，河南大学数学与统计学院2018级本科生，主要从事医学图像处理研究，E-mail：joosenli@outlook.com

庞志峰: 博士，河南大学数学与统计学院副教授、博士生导师，主要从事医学图像处理中的数学理论及方法，E-mail：zhifengpang@163.com

通讯作者:
庞志峰*，

中图分类号: O 242；TP 391.41
计量
- 文章访问数: 547
- HTML全文浏览量: 201
- PDF下载量: 223
出版历程
- 收稿日期: 2022-05-08
- 修回日期: 2022-05-24
- 录用日期: 2022-06-10
- 网络出版日期: 2022-06-26
- 发布日期: 2022-11-02

A Variational Model for Removing Concentric Elliptical Artifacts from CT Images

1.
Henan University, Kaifeng 475004, China School of Mathematics and Statistics
2.
Henan University, Kaifeng 475004, China School of Computer and Information Engineering

摘要

摘要: 在计算机断层成像（CT）中，伪影会降低重建图像的质量。针对该问题，本文提出一种去除CT图像中同心椭圆伪影的方法。该方法基于方向全变分（DTV）的思想，将椭圆伪影的去除问题建模为能量最小化问题，并通过对椭圆伪影边缘特征的分析，建立适应于椭圆伪影的变分模型。由于提出的模型为具有可分裂结构的非光滑凸优化问题，因此本文使用交替方向乘子法（ADMM）。最后，通过仿真实验验证该模型对于去除椭圆伪影的有效性。
- CT影像 /
- 交替方向乘子法 /
- 椭圆伪影 /
- 非光滑问题
Abstract: In computed tomography (CT) imaging, artifacts will degrade the quality of reconstructed images. To solve this issue, in this paper we propose a method to remove concentric elliptical artifacts from CT images. This method is based on the idea of Directional total variation (DTV), which models the problem of elliptical artifact removal as an energy minimization problem, and establishes a variation-based model which is adapted the elliptical artifacts by analyzing the edge features of elliptical artifacts. Since the proposed model is a non-smooth convex optimization problem with a divisible structure, the alternating direction multiplier method (ADMM) is applied. Finally, the effectiveness of the model in removing elliptical artifacts is verified by simulation experiments.
- CT images /
- alternating direction multiplier method /
- elliptical artifacts /
- nonsmooth problem

HTML全文

图 1 椭圆几何关系示意图，其中子图（a）中椭圆长轴在x轴上，子图（b）中椭圆长轴在y轴上

Figure 1. Schematic diagram of the geometric relationship of the ellipse, the long axis of the ellipse in subfigure (a) is on the x-axis and the long axis of the ellipse in subfigure (b) is on the y-axis

下载: 全尺寸图片幻灯片

图 2 去伪影前后Shepp-Logan模体及其ROI，第1行为参考图像，第2行为被伪影污染的图像，第3行为去伪影后的图像

Figure 2. Shepp-Logan phantom and its ROI before and after artifact removal, the first row is the reference image, the second row is the image contaminated with artifacts, and the third row is the artifact-removed image

下载: 全尺寸图片幻灯片

图 3 像素对比图，其中红色折线表示原始图像灰度值，蓝色折线表示含伪影图像灰度值，绿色折线表示去伪影后图像灰度值

Figure 3. Pixel comparison chart, the red line indicates the gray value of the reference image, blue line indicates the gray value of the image with artifacts, and green line indicates the gray value of the image after removing artifacts

下载: 全尺寸图片幻灯片

图 4 去伪影前后胸腔CT及其ROI，第1行为原始图像，第2行为被伪影污染的图像，第3行为去伪影后的图像

Figure 4. Chest CT and its ROI before and after artifact removal. The first row is the reference image, the second row is the image contaminated with artifacts, and the third row is the artifact-free image

下载: 全尺寸图片幻灯片

表 1 算法1

Table 1 Algorithm 1

　　　　算法1：使用ADMM解决问题（4）

　　　　1. 初始化：

$\lambda > 0,\;\,{\gamma _1} > 0,\;\,{\gamma _2} > 0$ ，选择

${{\boldsymbol{f}}^0},\,\;{{\boldsymbol{v}}^0},\,\;{{\boldsymbol{\alpha}} ^0}$ 和

${{\boldsymbol{\beta}} ^0}$ 的初始值
　　　　2. 对于

$k = 1,\;2,\; \cdots$ 通过（7），（10）和（13）依次获得

${{\boldsymbol{w}}^{k + 1}},\;{{\boldsymbol{v}}^{k + 1}},\;{{\boldsymbol{f}}^{k + 1}}$
　　　　3. 直到满足

$\frac{ { { {\left\| { {{\boldsymbol{f}}^k} - {{\boldsymbol{f}}^{k - 1} } } \right\|}_2} } }{ { { {\left\| { {{\boldsymbol{f}}^{k - 1} } } \right\|}_2} } } \leq {10^{ - 5} }$ 或

$k \geq 500$ 时终止
　　　　4. 将

${\boldsymbol{f}}: = {{\boldsymbol{f}}^{k + 1}}$ 作为输出图像

下载: 导出CSV

表 2 去伪影前后Shepp-Logan模体的SSIM和PSNR对比

Table 2 Comparison of SSIM and PSNR of Shepp-Logan phantom before and after artifact removal

对应图像	Shepp-Logan模体
对应图像	SSIM（含伪影）	SSIM（不含伪影）	PSNR（含伪影）	PSNR（不含伪影）
（g）、（m）	0.990	0.997	49.052	51.442
（i）、（o）	0.961	0.984	44.178	48.122
（j）、（p）	0.981	0.992	46.369	49.611
（k）、（q）	0.989	0.997	46.150	47.742
（l）、（r）	0.963	0.988	43.389	47.108

下载: 导出CSV

表 3 去伪影前后胸腔CT的SSIM和PSNR对比

Table 3 Comparison of SSIM and PSNR of chest CT before and after artifact removal

对应图像	Shepp-Logan 模体
对应图像	SSIM（含伪影）	SSIM（不含伪影）	PSNR（含伪影）	PSNR（不含伪影）
（g）、（m）	0.619	0.655	32.472	34.238
（i）、（o）	0.917	0.940	32.984	33.371
（j）、（p）	0.833	0.828	34.254	35.229
（k）、（q）	0.933	0.954	33.328	34.801
（l）、（r）	0.859	0.874	34.766	34.156

下载: 导出CSV

参考文献(19)

[1]	WANG G, YU H, de MAN B. An outlook on X-ray CT research and development[J]. Medical Physics, 2008, 35(3): 1051−1064. doi: 10.1118/1.2836950
[2]	汤少杰, 张砚博, 汪友明, 等. 可同时抑制多种图像伪影的最优骨校正[J]. CT理论与应用研究, 2018,27(3): 301−314. DOI: 10.15953/j.1004-4140.2018.27.03.03. TANG S J, ZHANG Y B, WANG Y M, et al. An optimal bone correction capable of simultaneously suppressing various types of image artifacts[J]. CT Theory and Applications, 2018, 27(3): 301−314. DOI: 10.15953/j.1004-4140.2018.27.03.03. (in Chinese).
[3]	黄铜港, 李保磊, 汤少杰, 等. 基于双域滤波与距离变换的螺旋CT图像风车伪影校正[J]. 中国体视学与图像分析, 2021,26(2): 123−133. doi: 10.13505/j.1007-1482.2021.26.02.003 HUANG T G, LI B L, TANG S J, et al. Windmill artifact reduction for helical CT based on dual-domain filtering and distance transform[J]. Chinese Journal of Stereology and Image Analysis, 2021, 26(2): 123−133. (in Chinese). doi: 10.13505/j.1007-1482.2021.26.02.003
[4]	韩泽芳, 上官宏, 张雄, 等. 基于深度学习的低剂量CT成像算法研究进展[J]. CT理论与应用研究, 2022,31(1): 117−134. DOI: 10.15953/j.1004-4140.2022.31.01.14. HAN Z F, SHANGGUAN H, ZHANG X, et al. Advances in research on low-dose CT imaging algorithm based on deep learning[J]. CT Theory and Applications, 2022, 31(1): 117−134. DOI: 10.15953/j.1004-4140.2022.31.01.14. (in Chinese).
[5]	陈昶羽, 高河伟, 张涛, 等. CT解析重建方法进展: 从圆轨迹扫描到多源直线扫描成像[J]. CT理论与应用研究, 2021,30(2): 263−277. DOI: 10.15953/j.1004-4140.2021.30.02.14. CHEN C Y, GAO H W, ZHANG T, et al. Progress on analytical CT reconstruction methods: From circular trajectory scanning to multi-source linear trajectory scanning imaging[J]. CT Theory and Applications, 2021, 30(2): 263−277. DOI: 10.15953/j.1004-4140.2021.30.02.14. (in Chinese).
[6]	SADI F, LEE S Y, HASAN M K. Removal of ring artifacts in computed tomographic imaging using iterative center weighted median filter[J]. Computers in Biology and Medicine, 2010, 40(1): 109−118. doi: 10.1016/j.compbiomed.2009.11.007
[7]	NATTERER F, RITMAN E L. Past and future directions in X-ray computed tomography (CT)[J]. International Journal of Imaging Systems and Technology, 2002, 12(4): 175−187. doi: 10.1002/ima.10021
[8]	张华, 黄魁东, 史仪凯, 等. 一种基于空气扫描的锥束CT环形伪影校正方法[J]. CT理论与应用研究, 2012,21(2): 247−254. ZHANG H, HUANG K D, SHI Y K, et al. Artifact correction method based on air scan for cone-beam CT[J]. CT Theory and Applications, 2012, 21(2): 247−254. (in Chinese).
[9]	KAK A C, SLANEY M. Principles of computerized tomographic imaging[M]. IEEE. Press, 1989.
[10]	ZHAO S, LI J, HUO Q. Removing ring artifacts in CBCT images via generative adversarial network[C]//2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2018: 1055-1059.
[11]	SIJBERS J, POSTNOV A. Reduction of ring artefacts in high resolution micro-CT reconstructions[J]. Physics in Medicine and Biology, 2004, 49(14): N247−253. doi: 10.1088/0031-9155/49/14/N06
[12]	CHEN Y W, DUAN G, FUJITA A, et al. Ring artifacts reduction in cone-beam CT images based on independent component analysis[C]//2009 IEEE Instrumentation and Measurement Technology Conference. IEEE, 2009: 1734-1737.
[13]	KYRIAKOU Y, PRELL D, KALENDER W A. Ring artifact correction for high-resolution micro CT[J]. Physics in Medicine & Biology, 2009, 54(17): N385.
[14]	YAN L, WU T, ZHONG S, et al. A variation-based ring artifact correction method with sparse constraint for flat-detector CT[J]. Physics in Medicine & Biology, 2016, 61(3): 1278.
[15]	MURATA K, OGAWA K. Ring-artifact correction with total-variation regularization for material images in photon-counting CT[J]. IEEE Transactions on Radiation and Plasma Medical Sciences, 2020, 5(4): 568−577.
[16]	SALEHJAHROMI M, WANG Q, GJESTEBY L A, et al. A directional TV based ring artifact reduction method[C]//Medical Imaging 2019: Physics of Medical Imaging. SPIE, 2019, 10948: 593-599.
[17]	LI Y, ZHAO Y, JI D, et al. Sparse-domain regularized stripe decomposition combined with guided-image filtering for ring artifact removal in propagation-based X-ray phase-contrast CT[J]. Physics in Medicine Biology, 2021, 66(10): 105011.
[18]	PANG Z F, ZHOU Y M, WU T, et al. Image denoising via a new anisotropic total-variation-based model[J]. Signal Processing: Image Communication, 2019, 74: 140−152. doi: 10.1016/j.image.2019.02.003
[19]	BAYRAM I, KAMASAK M E. A directional total variation[C]//2012 Proceedings of the 20th European Signal Processing Conference (EUSIPCO). IEEE, 2012: 265-269.