基于l（0）梯度最小化的有限角度CT图像重建_图像梯度L

151 浏览量 2021-04-04 08:39:57 上传评论 1 收藏 1.37MB PDF 举报

在计算机断层摄影（CT）成像的医学和工业应用中，受扫描环境和对患者施加过多X射线辐射的风险所限制，从有限的投影数据重建高质量的CT图像已成为热门话题。在有限的扫描角度范围内进行X射线成像是一种有效的成像方式，可以减少对患者的辐射剂量。由于此模式中可用的投影数据不完整，因此有限角度CT图像重建实际上是一个不适定的逆问题。为了解决该问题，通过常规的滤波反投影（FBP）算法重建的图像经常在边缘附近产生明显的条纹伪影和逐渐变化的伪影。基于总变化量最小化（TVM）的图像重建可以显着减少少数视图CT中的条纹伪影，但受限于有限角度CT中边缘附近的伪影逐渐变化。为了抑制这种伪像，我们针对有限角度CT开发了一种基于l（0）梯度最小化的图像重建算法。在已开发的重建模型框架内，将图像梯度的l（0）-范数作为正则化函数。我们将优化问题转化为几个优化子问题，然后以交替迭代的方式解决了这些子问题。进行了数值实验，以验证所开发算法的效率和可行性。根据性能评估的峰峰值信噪比（PSNR）和归一化均方根距离（NRMSD）的统计分析结果，表明在不同扫描角度范围内，不同算法之间存在显着的统计学差异（p <0.0001）。从实验结果还可以看出，该算法在同时抑制边缘附近的条纹伪影和渐进伪影方面优于传统的重建算法。在计算机断层扫描（CT）成像领域，为了降低对患者不必要的X射线辐射，从有限的投影数据中重建高质量的图像是一项关键挑战。有限角度CT图像重建是解决这一问题的有效途径，它通过减少扫描角度来减少辐射剂量，但同时也带来了图像重建的困难。由于可用的投影数据不足，该过程面临一个不适定的逆问题，导致常规的滤波反投影（FBP）算法在重建图像时出现明显的条纹伪影和边缘附近的渐变伪影。为了解决这些问题，研究者提出了一种基于l（0）梯度最小化的图像重建方法。这种方法的核心在于利用图像梯度的l（0）-范数作为正则化手段。l（0）-范数不同于通常的l（2）-范数，它更倾向于找到稀疏解，即具有较少非零元素的解。在CT重建中，这有助于突出图像的重要特征，如边缘，同时抑制噪声和伪影。在所提出的算法中，优化问题被分解为多个子问题，然后通过交替迭代的方式解决。这样的策略有助于平衡图像细节的保留与伪影的去除。通过数值实验，新算法的效率和可行性得到了验证。实验结果通过峰峰值信噪比（PSNR）和归一化均方根距离（NRMSD）等指标进行了统计分析，结果显示在不同的扫描角度下，新算法与其他传统重建方法相比有显著的统计差异，并且在抑制条纹伪影和渐变伪影方面表现出优越性。此外，该研究的贡献还体现在为解决有限角度CT图像重建的不适定问题提供了一个新的视角。l（0）梯度最小化不仅减少了条纹伪影，还能有效处理边缘附近的渐变伪影，这对于提高图像质量，尤其是医疗诊断的准确性至关重要。未来的研究可能进一步优化这种算法，例如通过改进迭代策略或结合其他正则化技术，以实现更高效、更精确的图像重建。这篇研究论文展示了基于l（0）梯度最小化的图像重建算法在有限角度CT成像中的潜力，为减少辐射剂量的同时提升图像质量提供了新的解决方案。这种方法对于提升CT成像技术的临床应用价值以及在工业无损检测等领域都有重要意义。

资源推荐

资源详情

资源评论

RESEARCH ARTICLE

ℓ

Gradient Minimization Based Image

Reconstruction for Limited-Angle Computed

Tomography

Wei Yu

1,3

, Li Zeng

2,3

1 School of Biomedical Engineering, Hubei University of Science and Technology, Xianning, China,

2 College of Mathematics and Statistics, Chongqing University, Chongqing, China, 3 Engineering Research

Center of Industrial Computed Tomography Nondestructive Testing of the Education Ministry of China,

Chongqing University, Chongqing, China

* drlizeng@cqu.edu.cn

Abstract

In medical and industrial applications of computed tomography (CT) imaging, limited by the

scanning environment and the risk of excessive X-ray radiation exposure imposed to the

patients, reco nstructing high quality CT images from limited projection data has become a

hot topic. X-ray imaging in limited scanning angular range is an effective imaging modality

to reduce the radiation dose to the patients. As the projection data available in this modality

are incomplete, limited-angle CT image reconstruction is actually an ill-posed inverse prob-

lem. To solve the problem, image reconstructed by conventional filtered back projection

(FBP) algori thm frequently results in conspicuous streak artifacts and gradual changed arti-

facts nearby edges. Image reconstruction based on total variation minimization (TVM) can

significantly reduce streak artifacts in few-view CT, but it suffers from the gradual changed

artifacts nearby edges in limited-angle CT. To suppress this kind of artifacts, we develop an

image reconstruction algorithm based on ℓ

gradient minimization for limited-angle CT in

this paper. The ℓ

-norm of the image gradient is taken as the regularization function in the

framework of developed reconstruction model. We transformed the optimization problem

into a few optimization sub-problems and then, solved these sub-problems in the man ner of

alternating iteration. Numerical experiments are performed to validate the ef ficiency and the

feasibility of the developed algorithm. From the statistical analy sis results of the perfor-

mance evaluations peak signal-to-noise ratio (PSNR) and normalized root mean square

distance (NRMSD), it shows that there are significant statistical differences between differ-

ent algorithms from different scanning angular ranges (p<0.0001). From the experimental

results, it also indicates that the developed algorithm outperforms classical reconstruction

algorithms in suppressing the streak artifacts and the gradua l changed artifacts nearby

edges simultaneously.

PLOS ONE | DOI:10.1371/journal.pone.0130793 July 9, 2015 1/15

OPEN ACCESS

Citation: Yu W, Zeng L (2015) ℓ

Gradient

Minimization Based Image Reconstruction for

Limited-Angle Computed Tomography. PLoS ONE

10(7): e0130793. doi:10.1371/journal.pone.0130793

Editor: Huafeng Liu, Zhejiang Univ, CHINA

Received: February 5, 2015

Accepted: May 26, 2015

Published: July 9, 2015

article distributed under the terms of the Creative

Commons Attribution License, which permits

unrestricted use, distribution, and reproduction in any

medium, provided the original author and source are

credited.

Data Availability Statement: All relevant data are

within the paper and its Supporting Information files.

Funding: This work is supported by the National

Natural Science Foundation of China under grant

(61271313) (http://www.nsfc.gov.cn), National

Instrumentation Program of China (2013YQ030629)

(http://www.most.gov.cn), and Chongqing science and

technology research plan project (cstc2012gg-

yyjs70016). The funders had no role in study design,

data collection and analysis, decision to publish, or

preparation of the manuscript.

Competing Interests: The authors have declared

that no competing interests exist.

Introduction

As an important nondestructive testing method, CT shows large-scale applications in many

fields such as medical diagnosis, industrial nondestructive testing, etc. In practical applications

of CT imaging, when projection data obtained are adequate and complete, the FBP algorithm,

which has been commonly utilized in commercial CT [1], can reconstruct images accurately.

However, limited by the scanning environment and the excessive radiation dose imposed to the

patients, it is desired that high quality CT images can be reconstructed from low-dose projec-

tion data [2,3,4]. To reduce the radiation dose to the patients, an effective imaging modality is

X-ray imaging in limited scanning angular range. It is possible that the effective scanning angu-

lar range doesn’t satisfy the condition of short scan [5], i.e., the effective scanning angular range

is less than 180° plus fan angle. In this case, significant streak artifacts and gradual changed arti-

facts nearby edges are present in reconstructed images by conventional FBP algorithm and con-

sequently, images are distorted [6]. In the medical domain, especially for dental CT [7,8], C-

arm tomosynthesis [9], imaging in the chest and the breast [10] etc., as X-ray ionizing radiation

is harmful to human bodies, it is in urgent need to use shorter time of exposure and fewer pro-

jection data to reconstruct approximately accurate images. Therefore, to reconstruct high-qual-

ity images using limited-angle projection data has been a research focus all along.

Recently, the iterative reconstruction algorithm shows more advantages than conventional

FBP algorithm in dealing with the reconstruction problem with incomplete projection data. As

early as 1980s, the algebraic reconstruction technique (ART) and simultaneous algebraic

reconstruction technique (SART) were utilized by some researchers to investigate CT image

reconstruction [11, 12]. While for incomplete projection data, obvious artifacts and noise are

present in reconstructed images obtained by the two algorithms.

In 1992, Rudin et al. proposed an image denoising method based on total variation (TV) of

image [13], and they showed that this method can well protect the edge during the denoising

process. Assuming that the pixel value of image at positio n (x,y) is labeled by u

x,y

, the TV of

image can be expressed as

jjujj

x;y

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

ðu

x;y

 u

x1;y

þðu

x;y

 u

x;y1

: ð1Þ

The TV is essentially the ℓ

-norm of the image gradient magnitude. In image domains,

images consisting of image gradient magnitudes are approximately sparse. To utilize the spar-

sity of gradient image, the TV norm can be taken as a regularization function. Furthermore, in

2006, Sidky et al.[14] adapted the TV minimization to consider the sparsity of the image gradi-

ent magnitudes, and then proposed an accurate algorithm for CT image reconstruction from

few-view and limited-angle projection data. This algorithm is called TVM based algorithm

hereafter. The TVM based algorithm can obtain accurate images from incomplete projections

especially in the sparse angular sampling over 360°. While the scanning angula r range is limited

and less than 180°(such as 90° and 120°), the reconst ruction results suffer from gradual

changed artifacts nearby the edges of the objects [14, 15], although it shows superiority to sup-

press streak artifacts. To further improve the quality of CT images for limited-angle tomogra-

phy, some scholars have advanced the conventional TV based image reconstruction algorithm

[16–18]. Although these methods improve the performance on reducing gradual changed arti-

facts nearby edges, however, the edge information of the objects may have a certain degree of

distortion. With the aim to make the most of previously reconstructed CT images, by means of

the constraint of TV, the reconstruction algorithms can generate better images [19,20], while

their applications are limited to some extent as the image database is often needed before

image reconstruction. Other reconstruction algorithms based on the prior knowledge of image

ℓ

Gradient Based Image Reconstruction for Limited-Angle Tomography

PLOS ONE | DOI:10.1371/journal.pone.0130793 July 9, 2015 2/15

coefficient sparsity in wavelet domains for limited-angle CT image reconstruction can be

found in [21–23]. In our work, we focus the regularization in the image domain just as TV reg-

ularization done. Thus, the TVM based reconstruction results are compared with our results.

In recent years, a novel regularization method based on the ℓ

-norm of image gradient has

been applied in the image smoothing [24], image segmentation [25], image super-resolution

and blur deconvolution [26], visual enhancement [27], disparity and optical flow partitioning

[28]. Different from the ℓ

-norm of image u,||u||

, which is the number of its non-zero coeffi-

cients, the ℓ

-norm of image gradient is denoted as

jjrujj

#fpjj@

jþj@

j 6¼ 0g; ð2Þ

where the gradient of 2D image at the pixel point p is denoted as ru

=(@

)

, @

and

represent the differences in x direction and in y direction respectively. #{} is counting

operator, counting the number of p that satisﬁes |@

|+|@

|6¼0. As the ℓ

-norm of image gra-

dient does not count on gradient magnitude, the large gradient magnitudes will not be penal-

ized, thus the edge can be effectively retained [24].

To better preserve the edges and suppress the artifacts to limited-angle CT image recon-

struction, we developed an alternating iterative reconstruction algorithm for limited-angle CT

based on ℓ

gradient minimization. In this paper, different from the ℓ

-norm of the image gra-

dient magnitude mentioned above, the ℓ

-norm of image gradient was taken as the regulariza-

tion function of the new optimization problem. We converted the optimization problem into a

few sub-problems, and solved these problems alternately. From the experimental results, it is

shown that by the developed algorithm the streak artifacts and gradual changed artifacts

nearby edges can be effectively reduced.

The rest of the paper is organized as follows. In section Method, our reconstruction algorithm

for limited-angle tomography is described, together with an efficient numerical scheme. More-

over, the performance evaluations are also outlined in this section. In the following section,

experimental results and discussion are presented and conclusions are given in final section.

Method

The fan-beam X-ray CT has been widely used in medical diagnosis, which will be the scanning

geometry that we focus in this paper. Fig 1 shows the scanning geometry configuration for cir-

cular and limited-angle fan-beam CT. For limited-angle tomography, in this paper, the scan-

ning angular range is limited within [0,θ], where θ is the maximum rotation angle of the X-ray

source, usually less than 180°.

As described in detail in S1 Appendix, we approximate the CT imaging model as following

discrete linear system [11]:

Au ¼ g ð3Þ

where u is the unknown object to be reconstructed, g is the measured projection data, A is the

system matrix which represents the forward projection.

In some practical CT imaging, when projection data are incomplete, the system Eq (3) is

underdetermined. To find the solution to this problem, we usually need to acquire the optimal

solution u



satisfying the optimization problem in the following form [29]:



¼ min

FðuÞ :¼ DðuÞþl  C ðuÞ: ð4Þ

where D(u) is data ﬁdelity term; C(u) represents the regularization term; λ is the penalty

parameter.

ℓ

Gradient Based Image Reconstruction for Limited-Angle Tomography

PLOS ONE | DOI:10.1371/journal.pone.0130793 July 9, 2015 3/15

剩余14页未读，继续阅读

评论收藏

内容反馈

weixin_38667408

粉丝: 8
资源: 896

基于l（0）梯度最小化的有限角度CT图像重建

使用图像梯度l（0）-范数和张量字典的低剂量光谱CT重建

基于加权总差分最小化的中子稀疏投影计算机断层重建方法

有限角度CT图像重建迭代算法研究1

研究论文-基于小波框架的有限角度CT重建算法.pdf

CT图像重建的迭代算法.zip

FTVd_v2.0.rar_全变差_全变差最小化_去噪_图像去噪_重建去噪

基于对抗式残差密集深度神经网络的CT稀疏重建.docx

基于偏微分方程的CT图像分割及其MATLAB实现.pdf

CT系统标定与有限角度CT重建方法的研究

基于卷积神经网络的有限视角CT重建.pdf

基于乘性正则化的有限角度CT重建算法

基于FPGA实现CT图像重建加速的设计.pdf

基于异构多GPU的锥束CT图像重建研究.pdf

基于序列子集共轭梯度的超分辨率图像重构

一种基于Contourlet变换与分裂Bregman方法的CT图像重建算法

平行束重建 ART

新建文件夹.zip_ART TV_ART 算法_MSE和SSIM_TV图像重建_art-tv

基于C++和opencv的CT图像重建系统源码.zip

基于同步辐射CT图像重建的对比度增强方法

基于字典学习的光谱CT图像重建

Matlab基于CT图像的三维头颅重建

基于Linux平台的CT图像重建的优势.pdf

基于ADMM的多GPU快速DBT迭代精准重建.pdf

具有纵向电视约束的基于字典学习的低剂量螺旋CT重建

通过多方向总变化从少量视图数据重建计算机断层扫描图像

最新资源