中国组织工程研究 ›› 2018, Vol. 22 ›› Issue (31): 4998-5002.doi: 10.3969/j.issn.2095-4344.0563

• 骨与关节图像与影像 bone and joint imaging • 上一篇    下一篇

实现稀疏角度下的精确CT重建:利用ADMM-LP算法求解非凸模型

宋 洁,陈 平,潘晋孝   

  1. 中北大学信息探测与处理山西省重点实验室,中北大学,山西省太原市  030051
  • 出版日期:2018-11-08 发布日期:2018-11-08
  • 通讯作者: 陈平,博士,教授,中北大学信息探测与处理山西省重点实验室,中北大学,山西省太原市 030051
  • 作者简介:宋洁,女,1994年生,山西省曲沃县人,汉族,山西省中北大学在读硕士,主要从事CT重建算法的研究。
  • 基金资助:

    国家自然科学基金(61571404,61601412);山西省高等学校优秀青年学术带头人支持计划

Reconstruction accuracy of sparse angle CT imaging: ADMM-CT algorithm based on LP-norm

Song Jie, Chen Ping, Pan Jin-xiao   

  1. Shanxi Provincial Key Laboratory of Signal Capturing and Processing, North University of China, Taiyuan 030051, Shanxi Province, China
  • Online:2018-11-08 Published:2018-11-08
  • Contact: Chen Ping, MD, Professor, Shanxi Provincial Key Laboratory of Signal Capturing and Processing, North University of China, Taiyuan 030051, Shanxi Province, China
  • About author:Song Jie, Master candidate, Shanxi Provincial Key Laboratory of Signal Capturing and Processing, North University of China, Taiyuan 030051, Shanxi Province, China
  • Supported by:

    the National Natural Science Foundation of China, No. 61571404 and 61601412; a grant from the Excellent Young Academic Leader Program of Shanxi Provincial Universities

摘要:

文章快速阅读:




文题释义:
LP范数:根据压缩感知理论,对于CT重建模型可以由一个保真项与一个正则项构成,以稀疏图像的LP范数为正则项的重建模型,可获取相较传统TV正则项更稀疏的解,使得在投影角度稀疏的条件下获取质量更高的重建图像。
交替方向乘子(ADMM)算法:ADMM法是一种求解优化问题的计算框架,通过分解协调过程,将大的全局问题分解为多个较小、较容易求解的局部子问题,并通过协调子问题的解而得到大的全局问题的解。在文中利用交替方向乘子法将多变量的非凸优化问题转化为针对子问题的优化问题,降低计算复杂度的同时减少求解难度。
 
摘要
背景:稀疏角度投影重建是减小CT辐射剂量的有效方法,但因其重建质量的问题限制了该方法的应用。
目的:研究基于LP范数的交替方向乘子-CT重建算法,旨在提高稀疏角度下的重建质量。
方法:将CT重建模型中的全变分正则项替换为非凸非光滑的LP范数正则项,并利用增广拉格朗日法将约束问题转化为无约束问题,再利用交替方向乘子框架结合广义收缩算法将原优化模型拆分为等价于原问题的子问题,最后迭代求解各子问题。
结果与结论:①通过仿真及实际实验,对比分析了全变分-凸集投影、代数重建-LP、Split-Bregman-LP以及所提算法在36个稀疏角度下的重建结果,结果显示论文提出的算法重建图像细节更完整,均方根误差更低,而且速度比Split-Bregman-LP快1倍;②说明提出的基于LP范数的交替方向乘子-LP算法,在投影角度稀疏情况下的重建结果具有较高的重建精度。

中国组织工程研究杂志出版内容重点:人工关节;骨植入物;脊柱骨折;内固定;数字化骨科;组织工程
ORCID: 0000-0001-5554-8549(宋洁)

关键词: X-CT稀疏角度重建, LP范数, 交替方向乘子法, 广义收缩算法, 迭代优化算法, 国家自然科学基金

Abstract:

BACKGROUND: Sparse-view CT imaging reconstruction is an effective method for reducing radiation dosage. But the reconstruction accuracy affects its promotion in clinic.

OBJECTIVE: To explore the availability of the alternating direction method of multipliers (ADMM)-CT reconstruction algorithm based on LP-norm, so as to improve the reconstruction accuracy of sparse angle CT imaging.
METHODS: To solve the optimized problem with gradient prior constraint, translate the constrained optimized problem into unconstrained optimization problem in the method of augmented Lagrange. Then, the ADMM could achieve the target that decomposed the optimized model into three sub-problems, which were equivalent to the original problem. Finally, the steepest descent method and the generalized shrinkage algorithm were used to solve the sub-problem separately.
RESULTS AND CONCLUSION: (1) Compared with the traditional TV-POCS algorithm, ART-LP algorithm and Split-Bregman-LP algorithm, the root-mean-square error of the proposed algorithm was lower and the details of the reconstruction image were more complete when projection numbers were 36. (2) To conclude, for sparse angles CT reconstruction, the proposed algorithm named ADMM-LP can obtain high image quality.

中国组织工程研究杂志出版内容重点:人工关节;骨植入物;脊柱骨折;内固定;数字化骨科;组织工程

Key words: Radiation Dosage, Tomography, X-Ray Computed, Tissue Engineering

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