北京航空航天大学学报 ›› 2017, Vol. 43 ›› Issue (11): 2316-2321.doi: 10.13700/j.bh.1001-5965.2017.0052

• 成像测量 • 上一篇    下一篇

压缩感知在电容层析成像中的应用

张立峰   

  1. 华北电力大学 自动化系, 保定 071003
  • 收稿日期:2017-02-06 修回日期:2017-04-24 出版日期:2017-11-20 发布日期:2017-09-18
  • 通讯作者: 张立峰 E-mail:hdlfzhang@126.com
  • 作者简介:张立峰,男,博士,副教授,硕士生导师。主要研究方向:电学层析成像技术。
  • 基金资助:
    国家自然科学基金(51306058);中央高校基本科研业务费专项资金(2017MS131)

Compressed sensing application to electrical capacitance tomography

ZHANG Lifeng   

  1. Department of Automation, North China Electric Power University, Baoding 071003, China
  • Received:2017-02-06 Revised:2017-04-24 Online:2017-11-20 Published:2017-09-18
  • Supported by:
    National Natural Science Foundation of China (51306058); the Fundamental Research Funds for the Central Universities (2017MS131)

摘要: 压缩感知(CS)理论是在充分利用信号稀疏性或可压缩性的情况下,对信号进行少量采样即可实现信号的精确重建。本文尝试将CS理论应用于电容层析成像(ECT)图像重建中,首先,使用快速傅里叶变换(FFT)基将原始图像灰度信号进行稀疏化处理;其次,将ECT灵敏度矩阵的各行按随机顺序进行排列,得到ECT系统随机观测矩阵;最后,选取当前普遍使用的基于内点法、梯度投影(GPSR)算法以及贪婪算法的CS图像重建算法进行ECT图像重建,并与线性反投影及Landweber迭代算法进行了对比。仿真实验结果表明:基于CS图像理论的ECT图像重建算法,其重建精度有所提高。本文同时分析了3种CS图像重建算法的优缺点及适用范围。

关键词: 电容层析成像(ECT), 图像重建, 压缩感知(CS), 内点法, GPSR算法, 贪婪算法

Abstract: Based on the sparsity or compressibility of the signal, compressed sensing (CS) theory can achieve high-accuracy reconstruction of the signal by sampling a small amount of data. In this paper, CS theory was used for the image reconstruction of electrical capacitance tomography (ECT). First, using the fast Fourier transformation (FFT) basis, the gray signals of original images can be transformed into the sparse signals. Then, the random observation matrix of ECT system was designed by rearranging the rows of the sensitivity matrix of ECT in a random order. Finally, interior point method, gradient projection for sparse reconstruction (GPSR) algorithm and greedy algorithm which are the three commonly used reconstruction algorithms of CS were used for ECT image reconstruction and the comparison was made with linear back projection algorithm and Landweber iterative algorithm. Simulation results indicate that reconstructed images with higher accuracy can be obtained using the ECT image reconstruction algorithm based on CS theory. Meanwhile, the advantages and disadvantages of the three CS image reconstruction algorithms were analyzed. The advice of selecting which type of image reconstruction algorithm was given.

Key words: electrical capacitance tomography (ECT), image reconstruction, compressed sensing (CS), interior point method, GPSR algorithm, greedy algorithm

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