L<sub>1</sub>范数字典约束的感兴趣区域CT图像重建算法

吴俊峰 1; 2; 牟轩沁 3

doi:10.7652/xjtuxb201902022

您当前的位置：

首页 >

文章列表页 >

L₁范数字典约束的感兴趣区域CT图像重建算法

更新时间：2025-07-09

- L₁范数字典约束的感兴趣区域CT图像重建算法
- A Reconstruction Algorithm of CT Images of Interested Regions Based on an L₁ Norm Dictionary Sparse Constraint
- 西安交通大学学报 2019年53卷第2期页码：163-169
- 作者机构：
  
  1. 西安理工大学理学院,西安,710048
  2. 东南大学计算机网络和信息集成教育部重点实验室,南京,210096
- 作者简介：
- 基金信息：
  
  : 2018-05-31。作者简介: 吴俊峰(1980—),女,博士,讲师。基金项目: 国家自然科学基金资助项目(61571359,61772416);东南大学计算机网络和信息集成教育部重点实验室开放基金资助项目(K93-9-2017-04)
- DOI：10.7652/xjtuxb201902022
  中图分类号： TN911.73
- 网络首发：2019-02-10，
  
  纸质出版：2019
- 稿件说明：
移动端阅览
吴俊峰 1, 2, 牟轩沁 3. L₁范数字典约束的感兴趣区域CT图像重建算法[J]. 西安交通大学学报, 2019,53(2):163-169. DOI: 10.7652/xjtuxb201902022.

A Reconstruction Algorithm of CT Images of Interested Regions Based on an L₁ Norm Dictionary Sparse Constraint[J]. 2019, 53(2): 163-169. DOI: 10.7652/xjtuxb201902022.
吴俊峰 1, 2, 牟轩沁 3. L₁范数字典约束的感兴趣区域CT图像重建算法[J]. 西安交通大学学报, 2019,53(2):163-169. DOI: 10.7652/xjtuxb201902022. DOI：

A Reconstruction Algorithm of CT Images of Interested Regions Based on an L₁ Norm Dictionary Sparse Constraint[J]. 2019, 53(2): 163-169. DOI: 10.7652/xjtuxb201902022. DOI：

摘要

针对现有全变分(TV)约束感兴趣区域(ROI)重建方法易产生块状伪影、细小结构丢失的问题

提出了一种L

范数字典稀疏约束的ROI低剂量CT医学图像重建算法。首先将ROI医学图像重建问题转化为最优化问题

以罚加权最小二乘函数为保真项

范数字典稀疏表示为约束项构建目标函数; 然后将目标函数分解为图像更新和字典稀疏表示两个子优化问题

并交替求解上述两个子优化问题

实现ROI图像重建。胸腔模体仿真实验结果表明

在分别添加光子数为1×10

、5×10

和1×10

泊松噪声投影情况下

与TV约束重建方法相比

图像结构相似度(SSIM)分别提高约0.103 5、0.113 1和0.125 8

峰值信噪比分别提高4.88、4.93和5.44 dB。山羊肺部实际CT扫描实验结果进一步证明

本文算法能够有效地去除块状伪影且较好的保留细小结构。

Abstract

A medical image reconstruction algorithm of CT images of interested region with low does based on an L

norm dictionary sparse constraint is proposed to address the problem that the existing total variation(TV)regularization algorithms often suffer from patchy artifacts and losing fine structure. First

ROI image reconstruction is converted into an optimization problem by using a penalized weighted least squares function to establish a data-fitting term and the L

norm of sparse representation in terms of learned dictionary as a constraint term. Then

the objective function is split into an image updating sub-optimi

zation problem and a sparse representation sub-optimization problem

and these two sub-problems are alternatively solved in a minimization manner. Chest simulation results and a comparison to the reconstruction algorithm with TV regularization show that in the cases of Poisson noise projection added 1×10

5×10

and 1×10

photons per detector element

respectively

the proposed algorithm decreases the structural similarity index metric by 0.103 5

0.113 1 and 0.125 8

respectively

and improves the peak signal to noise by 4.88

4.93 and 5.44 dB

respectivtly. Moreover

experiments with sheep Lung real CT validates that the proposed algorithm can effectively remove blocky artifacts and preserve low-contrast structures.

关键词

Keywords

references

WARD J P, LEE M, YE J C, et al. Interior tomography using 1D generalized total variation: part I Mathematical foundation [J]. SIAM Journal of Imaging Science, 2015, 8(4): 226-247.

WANG G, YU H Y. The meaning of interior tomography [J]. Physics in Medicine and Biology, 2013, 58(16): 161-186.

COURDURIER M, NOO F, DEFRISE M, et al. Solving the interior problem of computed tomography using a prior knowledge [J]. Inverse Problems, 2008, 24(6): 065001.

KUDO H, COURDURIER M, NOO F, et al. Tiny a priori knowledge solves the interior problem in computed tomography [J]. Physics in Medicine and Biology, 2008, 53(9): 2207-2225.

YU H Y, YE Y B, WANG G. Interior reconstruction using the truncated hilbert transform via singular value decomposition [J]. Journal of X-Ray Science and Technology, 2008, 16(4): 243-251.

JIN X, KATSEVICH A, YU H Y, et al. Interior tomography with continuous singular value decomposition [J]. IEEE Transactions on Medical Imaging, 2012, 31(11): 2108-2119.

LIU R, HE L, LUO Y, et al. Singular value decomposition-based 2D image reconstruction for computed tomography [J]. Journal of X-Ray Science and Technology, 2017, 25(1): 113-134.

YU H Y, WANG G. Compressed sensing based interior tomography [J]. Physics in Medicine and Biology, 2009, 54(9): 2791-2805.

YU H Y, YANG J S, JIANG M, et al. Supplemental analysis on compressed sensing based interior tomography [J]. Physics in Medicine and Biology, 2009, 54(18): 425-432.

XU Q, MOU X Q, WANG G, et al. Statistical interior tomography [J]. IEEE Transactions on Medical Imaging, 2011, 30(5): 1116-1128.

XU Q, YU H Y, MOU X Q, et al. Low-dose X-ray CT reconstruction via dictionary learning [J]. IEEE Transactions on Medical Imaging, 2012, 31(9): 1682-1697.

王爱齐, 徐坤, 宋爱民. 基于局部自相似的字典学习图像去噪方法 [J]. 大连交通大学学报, 2017, 38(4): 192-195.

WANG Aiqi, XU Kun, SONG Aimin. Image denoising by locally self-similarity dictionary learning [J]. Journal of Dalian Jiaotong University, 2017, 38(4): 192-195.

宋长明, 王赟. 融合低秩和稀疏表示的图像超分辨率重建算法 [J]. 西安交通大学学报, 2018, 52(7): 18-24.

SONG Changming, WANG Yun. Super resolution reconstruction algorithm combined low rank with sparse representation [J]. Journal of Xi'an Jiaotong University, 2018, 52(7): 18-24.

ELBAKRI I A, FESSLER J A. Statistical image reconstruction for polyenergetic X-ray computed tomography [J]. IEEE Transactions on Medical Imaging, 2002, 21(2): 89-99.

ELAD M, AHARON M. Image denoising via sparse and redundant representations over learned dictionaries [J]. IEEE Transactions on Image Processing, 2006, 15(12): 3736-3745.

MAIRAL J L, BACH F, PONCE J, et al. Online learning for matrix factorization and sparse coding [J]. Journal of Machine Learning Research, 2010, 11(1): 19-60.

JULIEN M. Spams-matlab-v2.5 [EB/OL].(2014-07-04)[2017-05-30].http:∥spams-devel.gforge.inria. fr/downloads.html.

毛宝林, 陈晓朝, 孝大宇, 等. 基于全变分最小化和快速一阶方法的低剂量CT有序子集图像重建 [J]. 物理学报, 2014, 63(13): 138701.

MAO Baolin, CHEN Xiaozhao, XIAO Dayu, et al. Ordered subset image reconstruction studied by means of total variation minimization and fast first-order method in low dose computed tomograhpy [J]. Acta Physica Sinica, 2014, 63(13): 138701.

LANGE K. Coordinate descent algorithms for LASSO penalized regression [J]. The Annals Applied Statistics, 2008, 2(1): 224-244.

WANG Z, BOVIK A C, SHEIKH H R, et al. Image quality assessment: from error visibility to structural similarity [J]. IEEE Transactions on Image Processing, 2004, 13(4): 600-612.

浏览量

下载量

CSCD

文章被引用时，请邮件提醒。

提交

工具集

关联资源

融合低秩和稀疏表示的图像超分辨率重建算法

面向高海拔空冷发电机防晕性能演化规律的电热耦合研究

三塔合一间接空冷系统结构参数对夏季运行特性的影响研究

采用机器学习的大规模并行程序I/O性能建模与预测方法

扇贝仿生密封腔室内超临界二氧化碳泄漏流湍动能耗散机理研究

L1范数字典约束的感兴趣区域CT图像重建算法

A Reconstruction Algorithm of CT Images of Interested Regions Based on an L1 Norm Dictionary Sparse Constraint

DOI：10.7652/xjtuxb201902022

摘要

Abstract

关键词

Keywords

references

L₁范数字典约束的感兴趣区域CT图像重建算法

A Reconstruction Algorithm of CT Images of Interested Regions Based on an L₁ Norm Dictionary Sparse Constraint