Image reconstruction based on total-variation minimization and alternating direction method in linear scan computed tomography

Linear scan computed tomography （LCT） is of great benefit to online industrial scanning and security inspection due to its characteristics of straight-line source trajectory and high scanning speed. However, in practical applications of LCT, there are challenges to image reconstruction due to limited-angle and insufficient data. In this paper, a new reconstruction algorithm based on total-variation （TV） minimization is developed to reconstruct images from limited-angle and insufficient data in LCT. The main idea of our approach is to reformulate a TV problem as a linear equality constrained problem where the objective function is separable, and then minimize its augmented Lagrangian function by using alternating direction method （ADM） to solve subproblems. The proposed method is robust and efficient in the task of reconstruction by showing the convergence of ADM. The numerical simulations and real data reconstructions show that the proposed reconstruction method brings reasonable performance and outperforms some previous ones when applied to an LCT imaging problem.

ON THE MONOTONE CONVERGENCE OF THE PROJECTED ITERATION METHODS FOR LINEAR COMPLEMENTARITY PROBLEMS

Under suitable conditions,the monotone convergence about the projected iteration method for solving linear complementarity problem is proved and the influence of the involved parameter matrix on the convergence rate of this method is investigated.

A New Iterative Solution Method for Solving Multiple Linear Systems

In this paper, a new iterative solution method is proposed for solving multiple linear systems A(i)x(i)=b(i), for 1≤ i ≤ s, where the coefficient matrices A(i) and the right-hand sides b(i) are arbitrary in general. The proposed method is based on the global least squares (GL-LSQR) method. A linear operator is defined to connect all the linear systems together. To approximate all numerical solutions of the multiple linear systems simultaneously, the GL-LSQR method is applied for the operator and the approximate solutions are obtained recursively. The presented method is compared with the well-known LSQR method. Finally, numerical experiments on test matrices are presented to show the efficiency of the new method.

Autofocus technique for ISAR imaging of uniformly rotating targets based on the ExCoV method

The inverse synthetic aperture radar (ISAR) imaging can be converted into a sparse reconstruction problem and solved by the l1norm minimization algorithm. The basis matrix in sparse ISAR imaging is usually characterized by the unknown rotation rate of a moving target, thus the rotation rate and the sparse signal should be jointly estimated. Especially due to the imperfect coarse motion compensation, we consider the phase error correction problem in the context of the sparse signal reconstruction. To address this issue, we propose an iterative reweighted method, which jointly estimates the rotation rate, corrects the phase error and reconstructs a high resolution ISAR image. The proposed method gives a gradual and interweaved iterative process to refine the unknown parameters to achieve the best sparse representation for the ISAR signals. Particularly, in ISAR image reconstruction, the l1norm minimization algorithm is sensitive to user parameters. Setting these user parameters are not trivial and the reconstruction performance depends significantly on their choices. Then, we consider an expansion-compression variance-component (ExCoV) based method, which is automatic and demands no prior knowledge about signal-sparsity or measurement-noise levels. Both numerical and electromagnetic data experiments are implemented to show the effectiveness of the proposed method. It is shown that the proposed method can estimate the rotation rate and correct the phase errors simultaneously, and its superior performance is proved in terms of high resolution ISAR image. © 2017 Beijing Institute of Aerospace Information.

A novel algorithm for transmission image reconstruction of tomographic gamma scaners

It is difficult to develop image reconstruction algorithms for tomographic gamma scanning based on drummed radioactive residues or wastes.In this paper,a novel reconstruction algorithm of transmission image for tomographic gamma scanning is proposed.It is based on the conventional transmission equation and equivalent gamma-ray track length modified by a Monte Carlo method.The algorithm is implemented by simulating the samples on the established platform.For the verification experiments of the algorithm,several cubic voxel samples were designed and manufactured.Experimental tests were conducted.The tomographic gamma scanning of transmission images is compared with the linear attenuation coefficients by the simulated values and experimental data with the algorithm and the reference values.The results show that the absolute relative errors of the reconstructed images are less than 5%.

SAR imaging method for sea scene target based on improved phase retrieval algorithm

Due to the influence of the platform random motion and electromagnetic propagation in turbulent media, the synthetic aperture radar (SAR) high resolution imaging for the sea scenes where there are large amounts of water returns with some target (land) returns is very difficult. To solve this problem, a SAR imaging method based on the improved phase retrieval (PR) algorithm is proposed. First, a filter is added to the conventional PR algorithm which can reduce the influence of water returns on the reconstruction of the targets and improve the reconstruction result of the targets. Then, the corrupted phase of the Fourier transform of the intensity image in the iterative process, which can improve the stability of the iterative algorithm, is used to reduce the recovery errors, and a better recovery performance is achieved. Finally, several experiments are performed to demonstrate the advantages of the proposed method. © 2016 Beijing Institute of Aerospace Information.

Randomized Kaczmarz algorithm for CT reconstruction

The order of the projection in the algebraic reconstruction technique(ART)method has great influence on the rate of the convergence.Although many scholars have studied the order of the projection,few theoretical proofs are given.Thomas Strohmer and Roman Vershynin introduced a randomized version of the Kaczmarz method for consistent,and over-determined linear systems and proved whose rate does not depend on the number of equations in the systems in 2009.In this paper,we apply this method to computed tomography(CT)image reconstruction and compared images generated by the sequential Kaczmarz method and the randomized Kaczmarz method.Experiments demonstrates the feasibility of the randomized Kaczmarz algorithm in CT image reconstruction and its exponential curve convergence.

基于两步迭代收缩法的多稀疏空间图像快速重构方法

由于多稀疏空间图像重构时,像素范围选取过大、峰值信噪比低以及重构时间长,导致图像重构方法存在重构效果差的问题,提出基于两步迭代收缩法的多稀疏空间图像快速重构方法。明确多稀疏空间图像重构存在的问题,在明确问题后,以迭代收缩阈值算法为基础,引入迭代加权收缩算法,结合每一轮迭代结果作为初值,完成图像重构的两步迭代收缩法设计,实现多稀疏空间图像快速重构。实验结果表明:应用该方法后的重构多稀疏空间图像峰值信噪比达到37.9 dB以上,图像重构时间仅为16.0 ms,图像结构相似性达到了0.98以上,并且重构多稀疏空间图像的效果更好,经过实验分析证实了所提方法具备可行性。

核酸检测的重排算法及其数值模拟

2022年春季上海遭受到奥密克戎变异株的侵袭,核酸检测是筛查新冠阳性病例的重要手段之一。目前社区常用核酸检测方式是10人/20人混合检测,重点人群单人单管复测。考虑到检测数量的庞大,二次复核易对非阳性人员造成恐慌,仿照CT成像原理,设计一种核酸检测重排方法,每人检测后将检测液分别随机置于多组不同试管中,根据不同组试管中的检测结果(投影数据),利用反投影方法,确定进入二次检测人员。计算机仿真结果表明,上述所设计的重排算法能够实现减少总检测数量和提高进入二次检测人员精度的目的。因此以上重排方法有望进一步应用到智能化的核酸采样机器人上,达到高效检测的目的。

ASIR算法对肝硬化患者碘摄入量、辐射剂量及门静脉CT图像质量的影响

目的 研究自适应统计迭代重建(ASIR)算法对肝硬化患者碘摄入量、辐射剂量及门静脉计算机断层扫描(CT)图像质量的影响。方法 以2020年1月至2022年12月河南中医药大学第一附属医院收治的68例肝硬化患者为研究对象,采用随机数字表法分为滤波反投影法(FBP)组(34例)和ASIR组(34例)。所有患者均进行门静脉CT检查,其中FBP组进行FBP重建(0%ASIR),对比剂用量450 mgI·kg^(-1),管电压100 kV;ASIR组进行ASIR重建(40%ASIR),对比剂用量350 mgI·kg^(-1),管电压100 kV。统计两组一般资料,比较两组碘摄入量、辐射剂量及门静脉CT、对比噪声比(CNR)、信噪比(SNR)值、图像质量主观评分。结果 ASIR组碘摄入量低于FBP组(P<0.05);ASIR组和FBP组有效剂量(ED)、CT剂量容积指数(CTDIvol)、剂量长度乘积(DLP)比较,差异无统计学意义(P>0.05)。ASIR组门静脉主干、右支、左支CT、CNR、SNR值及门静脉图像噪声、伪影、门静脉3级分支结构显示主观评分均高于FBP组(P<0.05)。结论 与FBP重建相比,ASIR重建用于肝硬化患者门静脉CT检查可提高门静脉CT、CNR、SNR值,提高CT成像的客观和主观图像质量,但可有效降低碘摄入量,且不会增加辐射剂量,有助于提高安全性。

医院图像分割和三维重建技术的研究

医学图像分割及三维重建技术是医学影像处理中的关键技术,可以帮助医生更准确地诊断和治疗疾病。我们通过举例对肺部CT图像进行分割和三维重建,探讨了其应用现状、技术原理和未来发展趋势。

基于曲波变换与联合方法的地震数据重建

野外地震数据采集通常会受地形等不可控因素的影响,导致采集到不规则缺失的地震数据,为了不影响后续地震资料处理,需要对缺失的地震数据进行重建。传统的重建算法往往收敛速度较慢,为此,提出将快速阈值迭代法和线性Bregman方法进行联合,在快速阈值迭代加速的基础上进一步提高了算法的效率,得到了一种快速高精度重建方法。在重建的过程中,以曲波域作为稀疏变换域,采用硬阈值函数和指数阈值模型。通过理论数据的模拟和实际数据的检验表明,相较于传统的地震数据重建方法,该方法重建的效果明显,重建效率更高。此外,该方法具有一定的抗噪性,在快速阈值迭代法高效收敛的基础上进一步加快了重建的效率。

基于1维子空间线性迭代射影重建

提出了一种基于1维子空间线性迭代的射影重建方法.该方法利用所有图像序列的行向量生成的子空间之和,与射影重建空间点的行向量生成的子空间是同一线性子空间,同时,由第1幅图像的3个行向量及另外一个行向量可以构成该线性子空间的一个基底的特性,线性迭代求取这个行向量及图像深度因子,最后完成射影重建.模拟实验和真实实验数据结果表明,该射影重建方法具有鲁棒性好、收敛性好以及重投影误差小等优点.

一种稳健的多源遥感图像特征配准方法

提出了一种稳健的多源遥感图像特征配准方法.首先引入相位一致性变换来消除图像灰度、对比度差异的影响并提取特征点;然后基于Zernike矩重构互相关函数并通过重构函数最大化实现图像旋转条件下的特征点匹配,同时结合双向最大互相关值匹配策略实现图像的粗略配准;最后,采用迭代修正变换参数算法最终实现多源遥感图像高精度配准.对大量多源图像进行配准实验表明,提出方法对多源遥感图像配准具有较强的适应性且配准精度高.

两相流参数测量ERT图像重建算法的研究

基于灵敏度理论建立了电阻层析成像(ERT)图像重建的数学模型,提出了一种将Tikhonov正则化技术和代数重建技术(ART)相结合的组合型ERT图像重建算法.研究表明,该算法较为稳定,能克服测量数据波动对图像重建的影响,同时仿真研究结果表明,与目前常用的灵敏度系数图像重建算法相比,该算法在图像重建质量方面得到了一定的改善.

线性迭代子空间射影重建法

该文提出了一种基于子空间线性迭代的射影重建方法,该方法利用所有的图像序列构成的行向量生成的线性子空间之和与射影重建结构点构成的行向量生成的子空间是同一线性子空间及在该子空间中任何一个基底都可以作为射影重建的特性,线性迭代地求取射影重建及图像深度因子。模拟实验和真实实验表明,该射影重建方法具有鲁棒性好、收敛性好及重投影误差小等优点。

基于Landweber迭代的图像重建算法

本文尝试将一种新型的基于Landweber迭代算法用于电阻抗断层图像（ＥＩＴ）重建．该算法与线性反投影算法不同，Landweber算法可以明显地改进图像质量．仿真结果表明，它不仅可以消除噪声干扰，而且能加快收敛速度．

一种具有迭代约束的最小二乘ECT图像重建算法

针对电容层析成像系统中的"软场"效应和病态问题,将最小二乘法和迭代法相结合,提出了一种最小二乘约束迭代的图像重建算法。给出了算法的数学模型,完成了算法的收敛性分析和证明,算法在图像重建中使迭代步长在保证收敛的情况下达到最优。仿真和实验结果表明,该方法与最小二乘法相比,具有更稳定、成像效果好等特点,为ECT图像重建提供了一种新的有效方法。

Monte-Carlo统计迭代图像重建算法

线性衰减系数图像重建是层析γ扫描(TGS)的一个核心问题。本文从粒子输运方程出发,应用Monte Carlo方法,提出了一种基于Monte Carlo方法的统计迭代图像重建算法。模拟结果表明,与一般TGS图像重建算法相比,该重建算法的重建图像误差大为减小,能够满足TGS装置的要求。

结合SLIC超像素和DBSCAN聚类的眼底图像硬性渗出检测方法

为自动检测出眼底图像中的硬性渗出,结合简单线性迭代聚类(SLIC)超像素分割算法和基于密度的聚类算法(DBSCAN),提出一种对眼底图像硬性渗出的检测方法.首先,采用SLIC超像素分割算法对彩色眼底图像进行过分割;然后,采用DBSCAN对上述分割得到的超像素进行聚类,形成簇;最后,分割出目标图像,并选用标准糖尿病视网膜病变数据库(DIARETDB0和DIARETDB1)的眼底图像验证上述组合算法的可行性.实验结果表明:算法能够快速、可靠地检测出眼底图像中的硬性渗出,具有可直接对彩色图像进行分割、特征提取的特点.