Skip to main content
SpringerLink
Log in

An Improved Conjugate Gradient Image Reconstruction Algorithm for Electromagnetic Tomography

  • Original Paper
  • Published:
Sensing and Imaging Aims and scope Submit manuscript

Abstract

Electromagnetic tomography (EMT) is an emerging imaging modality capable of visualizing the distribution of electrically conductive or magnetically permeable materials within the vessels and pipelines. Image reconstruction is the crucial step of EMT inverse problem, which is one of the main challenges in the promotion and application of EMT to industrial and biomedical fields. EMT inverse problem is ill-posed and ill-conditioned, which is the key to the reconstructed images quality. Tikhonov regularization is the widely used regularization method to solve the ill-posed problem. The revised Tikhonov regularization is obtained by improving the Tikhonov regularization when observation noise is considered. This paper presents an improved conjugate gradient algorithm based on the revised Tikhonov regularization to reduce the ill-posed nature of EMT inverse problem and enhance the spatial resolution of the reconstructed images. Numerical simulations results confirm that the quality of the reconstructed images obtained by the proposed algorithm is improved and also better than the other conventional algorithms including linear back projection, Tikhonov regularization algorithm, Landweber iterative algorithm, in terms of the typical patterns. Besides, correlation coefficients of the proposed ICGRT algorithm are 0.5961, 0.5989 and 0.5231 for three experimental typical patterns. The proposed ICGRT algorithm has highest correlation coefficients and reconstructs the best images.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Peyton, A. J., Yu, Z. Z., Lyon, G., Al-Zeibak, S., Ferreira, J., Velez, J., Linhares, F., Borges, A. R., Xiong, H. L., Saunders, N. H., & Beck, M. S. (1996). An overview of electromagnetic inductance tomography: Description of three different systems. Measurement Science Technology, 7, 261–271. https://doi.org/10.1088/0957-0233/7/3/006

    Article  Google Scholar 

  2. Ma, L., & Soleimani, M. (2017). Magnetic induction tomography methods and applications: A review. Measurement Science and Technology, 28, 1–12. https://doi.org/10.1088/1361-6501/aa7107

    Article  Google Scholar 

  3. Muttakin, I., Wondrak, T., & Soleimani, M. (2020). Magnetic induction tomography sensors for quantitative visualization of liquid metal flow shape. IEEE Sensors Letters, 4(7), 6001204. https://doi.org/10.1109/lsens.2020.3000292

    Article  Google Scholar 

  4. Soleimani, M., Li, F., Spagnul, S., Palacios, J., Barbero, J. I., Gutierrez, T., & Viotto, A. (2020). In situ steel solidification imaging in continuous casting using magnetic induction tomography. Measurement Science and Technology, 31, 065401. https://doi.org/10.1088/1361-6501/ab6f30

    Article  Google Scholar 

  5. Yin, W., & Peyton, A. J. (2006). A planar EMT system for the detection of faults on thin metallic plates. Measurement Science and Technology, 17, 2130–2135. https://doi.org/10.1088/0957-0233/17/8/011

    Article  Google Scholar 

  6. Yin, W., Chen, G., Chen, L., & Wang, B. (2011). The design of a digital magnetic induction tomography (MIT) system for metallic object imaging based on half cycle demodulation. IEEE Sensors Journal, 11, 2233–2240. https://doi.org/10.1109/jsen.2011.2128866

    Article  Google Scholar 

  7. Ma, L., & Soleimani, M. (2014). Hidden defect identification in carbon fibre reinforced polymer plates using magnetic induction tomography. Measurement Science and Technology, 25, 055404. https://doi.org/10.1088/0957-0233/25/5/055404

    Article  Google Scholar 

  8. Liu, Z., Li, W., Xue, F., Xiafang, J., Bu, B., & Yi, Z. (2015). Electromagnetic tomography rail defect inspection. IEEE Transactions on Magnetics, 51, 1–7. https://doi.org/10.1109/tmag.2015.2430283

    Article  Google Scholar 

  9. Wang, C., He, H., Cui, Z., Cao, Q., Zou, P., & Wang, H. (2018). A novel EMT system based on TMR sensors for reconstruction of permeability distribution. Measurement Science and Technology, 29, 104008. https://doi.org/10.1088/1361-6501/aad8ea

    Article  Google Scholar 

  10. Li, F., Soleimani, M., & Abascal, J. (2019). Planar array magnetic induction tomography further improvement. Sensor Review, 39(2), 257–268. https://doi.org/10.1108/sr-02-2018-0027

    Article  Google Scholar 

  11. Cui, Z., Chen, Y., & Wang, H. (2019). A dual-modality integrated sensor for electrical capacitance tomography and electromagnetic tomography. IEEE Sensors Journal, 19(21), 10016–10026. https://doi.org/10.1109/jsen.2019.2927629

    Article  Google Scholar 

  12. Xiao, Z., Tan, C., & Dong, F. (2019). 3-D hemorrhage imaging by cambered magnetic induction tomography. IEEE Transactions on Instrumentation and Measurement, 68(7), 2460–2468. https://doi.org/10.1109/tim.2019.2900779

    Article  Google Scholar 

  13. Chen, Y., Tan, C., & Dong, F. (2021). Combined planar magnetic induction tomography for local detection of intracranial hemorrhage. IEEE Transactions on Instrumentation and Measurement, 70, 4500111. https://doi.org/10.1109/tim.2020.3011621

    Article  Google Scholar 

  14. Xiang, J., Dong, Y., & Yang, Y. (2020). Multi-frequency electromagnetic tomography for acute stroke detection using frequency-constrained sparse bayesian learning. IEEE Transactions on medical imaging, 39(12), 4102–4112. https://doi.org/10.1109/tmi.2020.3013100

    Article  Google Scholar 

  15. Bakhsheshi, M. F., Ho, M., Keenliside, L., & Lee, T. Y. (2019). Non-invasive monitoring of brain temperature during rapid selective brain cooling by zero-heat-flux thermometry. Emerging Science Journal, 3(1), 1–9. https://doi.org/10.28991/esj-2019-01163

    Article  Google Scholar 

  16. Han, M., Cheng, X., & Xue, Y. (2016). Comparison with reconstruction algorithms in magnetic induction tomography. Physiological Measurement, 37, 683–697. https://doi.org/10.1088/0967-3334/37/5/683

    Article  Google Scholar 

  17. Cui, Z., Wang, Q., Xue, Q., Fan, W., Zhang, L., Cao, Z., Sun, B., Wang, H., & Yang, W. (2016). A review on image reconstruction algorithms for electrical capacitance/resistance tomography. Sensor Review, 36, 429–445. https://doi.org/10.1108/sr-01-2016-0027

    Article  Google Scholar 

  18. Xiao, J., Liu, Z., Zhao, P., Li, Y., & Huo, J. (2018). Deep learning image reconstruction simulation for electromagnetic tomography. IEEE Sensors Journal, 18(8), 3290–3298. https://doi.org/10.1109/jsen.2018.2809485

    Article  Google Scholar 

  19. Liu, X., Liu, Z., Li, Y., Zhao, P., & Wang, J. (2020). Research on direct 3D electromagnetic tomography technique. IEEE Sensors Journal, 20(9), 4758–4767. https://doi.org/10.1109/jsen.2020.2966274

    Article  Google Scholar 

  20. Zhaba, V., & Gohman, E. (2020). Activation level and probabilities of electromagnetic γ-transitions in the reaction 77Se(γ,γ’)77mSe. Emerging Science Journal, 4(3), 165–171. https://doi.org/10.28991/esj-2020-01220

    Article  Google Scholar 

  21. Prenga, D. (2020). General features of the q-XY opinion model. Journal of Human, Earth, and Future, 1(2), 87–96. https://doi.org/10.28991/hef-2020-01-02-05

    Article  Google Scholar 

  22. Ghorbani, R., & Nahvi, M. (2019). Analysis of performance of howland AC current source for electrical impedance spectro-tomography. Sensing and Imaging, 20, 28. https://doi.org/10.1007/s11220-019-0251-1

    Article  Google Scholar 

  23. Liu, X., & Liu, Z. (2019). A novel algorithm based on L1-Lp norm for inverse problem of electromagnetic tomography. Flow Measurement and Instrumentation, 65, 318–326. https://doi.org/10.1016/j.flowmeasinst.2019.01.010

    Article  Google Scholar 

  24. Liu, Z., He, M., & Xiong, H. (2005). Simulation study of the sensing field in electromagnetic tomography for two-phase flow measurement. Flow Measurement and Instrumentation, 16, 199–204. https://doi.org/10.1016/j.flowmeasinst.2005.02.008

    Article  Google Scholar 

  25. Li, F., Abascal, J., Desco, M., & Soleimani, M. (2017). Total variation regularization with split bregman-based method in magnetic induction tomography using experimental data. IEEE Sensors Journal, 17, 976–985. https://doi.org/10.1109/jsen.2016.2637411

    Article  Google Scholar 

  26. Wang, Q., Li, K., Zhang, R., Wang, J., Sun, Y., Li, X., Duan, X., & Wang, H. (2019). Sparse defects detection and 3D imaging base on electromagnetic tomography and total variation algorithm. Review of Scientific Instruments, 90, 124703. https://doi.org/10.1063/1.5120118

    Article  Google Scholar 

  27. Yuan, G., & Hu, W. (2018). A conjugate gradient algorithm for large-scale unconstrained optimization problems and nonlinear equations. Journal of Inequalities and Applications, 2018(1), 113. https://doi.org/10.1186/s13660-018-1703-1

    Article  MathSciNet  MATH  Google Scholar 

  28. Zhu, Z., Ma, J., & Zhang, B. (2020). A new conjugate gradient hard thresholding pursuit algorithm for sparse signal recovery. Computational and Applied Mathematics, 39(4), 270. https://doi.org/10.1007/s40314-020-01313-5

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The work is supported by Scientific and technological research project in Henan Province (No. 212102210620) and Doctoral Research Fund (No. 2020BSJJ006).

Author information

Authors and Affiliations

  1. School of Electrical and Information Engineering, Zhengzhou University of Light Industry, Zhengzhou, 450002, China

    Xianglong Liu

  2. School of Mechatronics and Vehicle Engineering, Zhengzhou University of Technology, Zhengzhou, 450044, China

    Ying Wang

Authors
  1. Xianglong Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ying Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xianglong Liu.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, X., Wang, Y. An Improved Conjugate Gradient Image Reconstruction Algorithm for Electromagnetic Tomography. Sens Imaging 23, 5 (2022). https://doi.org/10.1007/s11220-021-00374-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11220-021-00374-y

Keywords

Search

Navigation