北京航空航天大学学报 ›› 2018, Vol. 44 ›› Issue (8): 1569-1576.doi: 10.13700/j.bh.1001-5965.2017.0651

• 论文 • 上一篇    下一篇

一种电磁层析图像快速重建算法

刘泽, 肖君, 刘向龙, 赵鹏飞, 李勇, 霍继伟   

  1. 北京交通大学 电子信息工程学院, 北京 100044
  • 收稿日期:2017-10-23 修回日期:2017-12-01 出版日期:2018-08-20 发布日期:2018-08-29
  • 通讯作者: 刘泽 E-mail:zliu@bjtu.edu.cn
  • 作者简介:刘泽,男,博士,教授。主要研究方向:过程参数检测、电磁层析成像;肖君,女,硕士研究生。主要研究方向:电磁层析成像。
  • 基金资助:
    国家自然科学基金(61771041)

An algorithm for fast reconstruction of electromagnetic tomography images

LIU Ze, XIAO Jun, LIU Xianglong, ZHAO Pengfei, LI Yong, HUO Jiwei   

  1. School of Electronic Information Engineering, Beijing Jiaotong University, Beijing 100044, China
  • Received:2017-10-23 Revised:2017-12-01 Online:2018-08-20 Published:2018-08-29
  • Supported by:
    National Natural Science Foundation of China (61771041)

摘要: 针对电磁层析成像(EMT)逆问题中,灵敏度矩阵的病态性、不适定性等问题,提出了一种新的电磁层析图像快速重建算法。利用主成分分析(PCA)对灵敏度矩阵做降维映射,再利用奇异值分解(SVD)求广义逆矩阵,重建图像。在选取灵敏度矩阵的协方差矩阵的特征值个数中,利用灵敏度矩阵特有的多样本特性,提出图像相关系数最大化算法,更加合理地去除灵敏度矩阵中的冗余信息,在尽可能不丢失成像特征信息的条件下,提高了解稳定性。实际采集数据成像时,该算法只需一次矩阵乘法运算,为快速实时成像提供了可能。与传统单步算法和迭代算法相比,该算法在成像质量和速度上都有较明显优势。

关键词: 电磁层析成像(EMT), 主成分分析(PCA), 奇异值分解(SVD), 图像相关系数最大化, 降维

Abstract: For the inverse problem of electromagnetic tomography (EMT), the pathological and ill posed problems of the sensitivity matrix are discussed. A new electromagnetic tomography image reconstruction algorithm is proposed for this situation. Firstly, the principal component analysis (PCA) is used to reduce the dimension of the sensitivity matrix, and then the singular value decomposition (SVD) is used to calculate the generalized inverse matrix to reconstruct the image. After the covariance matrix of the sensitivity matrix is obtained, we need to compute the number of eigenvalues that the covariance matrix should retain. Then the maximization of the image correlation coefficient algorithm is proposed to solve it by using the unique multi-sample characteristics of the sensitivity matrix. It is more reasonable for sensitivity matrix to remove redundant information. And it improves the stability of the solution as far as possible without losing imaging feature information. When the actual data is used for imaging, this algorithm needs only one matrix multiplication, which provides the possibility for fast real-time imaging. In conclusion, compared with the traditional single step algorithm and iterative algorithm, the proposed algorithm has obvious advantages in both imaging quality and speed.

Key words: electromagnetic tomography (EMT), principal component analysis (PCA), singular value decomposition (SVD), image correlation coefficient maximization, dimensionality reduction

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