基于改进两步正则化算法的磁粒子成像重建方法研究

汤云东; 刘术; Rodolfo C. C. Flesch; 金涛

doi:10.12263/DZXB.20240084

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基于改进两步正则化算法的磁粒子成像重建方法研究

学术论文 | 更新时间：2024-09-23

- 基于改进两步正则化算法的磁粒子成像重建方法研究
- Research on Magnetic Particle Imaging Reconstruction Method Based on an Improved Two-Step Regularization Algorithm
- 电子学报 2024年页码：1-13
- 作者机构：
  
  1.福州大学物理与信息工程学院,福建福州 350108
  2.桑塔卡塔琳娜联邦大学自动化与系统系,弗洛里亚诺波利斯 88040-900
  3.福州大学电气工程与自动化学院,福建福州 350108
- 作者简介：
  
  [ "汤云东男，1981年出生于福建省宁德市，现为福州大学物理与信息工程学院副研究员，博士生导师.主要研究方向为生物医学信息处理与系统等.E-mail: tangyundong@fzu.edu.cn" ]
  [ "刘术女，2000年12月出生于湖北省荆州市.现为福州大学物理与信息工程学院研究生. 主要研究方向为生物医学信息处理与系统.E-mail: 221127073@fzu.edu.cn" ]
  [ "鲁道夫 C.C. 弗莱施男，1986 年出生于巴西，现为桑塔卡塔琳娜联邦大学教授，博士生导师. 主要研究方向为系统控制和自动化工程等. E-mail: rodolfo.flesch@ufsc.br" ]
  [ "金涛男，1976年出生湖北省宜昌市，现为福州大学电气工程与自动化学院教授，主要研究方向为智能信息处理及新能源电力电子技术等. Email:jintly@fzu.edu.cn" ]
- 基金信息：
  
  国家自然科学基金(62071124);巴西国家技术发展委员会(315546/2021-2)
- DOI：10.12263/DZXB.20240084
  中图分类号： TP391;R3
- 收稿：2024-01-18，
  
  修回：2024-06-04，
  
  网络出版：2024-09-23，
  
  纸质出版：2024-10-25
- 稿件说明：
移动端阅览
汤云东, 刘术, Rodolfo C. C. Flesch, 等. 基于改进两步正则化算法的磁粒子成像重建方法研究[J]. 电子学报, 2024, 52(10): 1-13.

TANG Yun-dong, LIU Shu, FLESH Rodolfo C. C., et al. Research on Magnetic Particle Imaging Reconstruction Method Based on an Improved Two-Step Regularization Algorithm[J]. Acta Electronica Sinica, 2024, 52(10): 1-13.
汤云东, 刘术, Rodolfo C. C. Flesch, 等. 基于改进两步正则化算法的磁粒子成像重建方法研究[J]. 电子学报, 2024, 52(10): 1-13. DOI：10.12263/DZXB.20240084

TANG Yun-dong, LIU Shu, FLESH Rodolfo C. C., et al. Research on Magnetic Particle Imaging Reconstruction Method Based on an Improved Two-Step Regularization Algorithm[J]. Acta Electronica Sinica, 2024, 52(10): 1-13. DOI：10.12263/DZXB.20240084

摘要

磁粒子成像（Magnetic Particle Imaging，MPI）是一种利用磁性纳米粒子非线性磁化响应实现高时空分辨率的成像技术，而MPI图像重建方法则可实现将测量得到的电压分布转换为可视的磁粒子浓度分布.现有系统矩阵法可较可靠地实现成像视场中单一浓度磁性颗粒图像重建，而对于不同浓度情况的图像重建则可采用两步正则化算法进行成像.然而，以往两步正则化算法因重建过程分成两步而增加了重建时长，同时筛选频率分量时通常只考虑了系统矩阵计算的信噪比，而未充分考虑实测电压信号的噪声因素.为改善这些问题，本文提出了基于ESD（Energy Spectral Density）特性和L曲线法优化的改进两步正则化算法，其可根据测量电压信号的ESD特性对频率分量进行降序排列，并根据压缩率筛选频率分量，以选出噪声水平低的频率分量从而减少噪声.同时，频率分量的减少也可使得重建时间的有效减少.此外，正则化过程中利用L曲线法选取最优正则化参数，也可一定程度减少重建过程中产生的噪声.仿真实验结果表明本文所提的算法在压缩率为0.6的情况下，重建图像质量在SSIM（Structure Similarity Index Measure）和NRMSE（Normalized Root Mean Square Error）上相比传统两步正则化算法分别提升了56.4%和22.3%，重建时间则缩短了39.8%.同时，实测结果也表明，本文的算法对于重建质量有所提升.当压缩率从1减小至0.1的过程中，重建质量无明显变化，但重建时间明显缩短.

Abstract

Magnetic particle imaging (MPI) is an imaging technique that utilizes the nonlinear magnetization response of magnetic nanoparticles to achieve high spatiotemporal resolution. The MPI image reconstruction method can convert the measured voltage distribution into the magnetic particles concentration distribution with visible image. The existing system matrix method can reliably reconstruct images for single concentration magnetic particles in the imaging field of view

while two-step regularization algorithm can be used for the image reconstruction under different concentration conditions. However

traditional two-step regularization algorithm increased the reconstruction time due to the two-step reconstruction process. Furthermore

it usually only considered the signal-to-noise ratio calculated by the system matrix during selecting frequency components but not fully considered the noise factor of the measured voltage signal. To address these issues

this paper proposes an improved two-step regularization algorithm based on the ESD (Energy Spectral Density) characteristics and L-curve optimization. This method can sort in descending order for frequency components by the ESD characteristics of measured voltage signal

and reduces the noise by selecting the frequency components with low noise levels after screening frequency components based on compression ratio. Meanwhile

the reduction of frequency components can also effectively reduce the reconstruction time for MPI image. In addition

the regularization process selects the optimal regularization parameters by using the L-curve method

and can also reduce the noise generated during the reconstruction process to a certain extent. The experimental results show that the proposed method by this study can improve the reconstructed image quality by 56.4% in SSIM (Structure Similarity Index Measure) and by 22.3% in NRMSE (Normalized Root Mean Square Error) under a compression rate of 0.6 with respect to traditional two-step regularization algorithms. In addition

the reconstruction time can be shortened by 39.8% compare to the traditional case. Meanwhile

the measured results also show that the proposed algorithm can help to improve the quality of reconstruction

and can also significantly shorten the reconstruction time with the similar quality when the compression ratio decreases from 1 to 0.1.

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基于Tikhonov正则化的高分辨率群时延测量与计算方法