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Microwave Tomography: A Numerical Study of Solving Linear Equations in the Non-linear Inverse Scattering Problem

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Microwave tomography is an inverse scattering problem which is formalized by determines the position and dielectric properties distribution of the unknown object from the measured scattered field. The quantitative image obtained from microwave tomography approach provides information directly correlated to the internal structure and composition of the examined object, which is necessity in biomedical and geo-surveying applications. Recently, studies on microwave imaging (MWI) for early breast cancer detection have attracted attentions. The breast cancer detection based on microwave tomography relies on large differences in dielectric properties between healthy and malignant tissues. In MWI, the examined object is successively illuminated by transmitting antenna and the resulting electromagnetic field is measured by the receiving antennas. The image reconstruction process in microwave tomography involves forward problem and inverse problem. For the forward problem, Method of Moment (MoM) is used to obtain the measurement data, which are related to the scattered field resulting from the interaction between the known incident field and the scatterers inside the imaging region. The measurement data is then used in the inverse problem, where Distorted Born Iterative Method (DBIM) is proposed to reconstruct the dielectric properties distribution of the object by solving the non-linear inverse scattering problem. The simulation results show that the ill-posedness of the non-linear problem can be reduced and a more stable solution can be performed by choosing the appropriate solving techniques of the system of linear equations.


  • Microwave tomography
  • Inverse scattering
  • Method of moment
  • DBIM
  • Non-linear

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  1. Nikolova, N.K.: Microwave imaging for breast cancer. IEEE Microw. Mag. 12(7), 78–94 (2011)

    CrossRef  Google Scholar 

  2. Ono, Y., Mohamed, L., Kuwahara, Y.: Optimization of configuration on imaging sensor for microwave tomography. In: Proceedings of the 2016 IEICE Society Conference, 2016, vol. C-2-79, no. ISSN 1349-144X

    Google Scholar 

  3. Mohamed, L., Ozawa, N., Ono, Y., Kamiya, T., Kuwahara, Y.: Study of correlation coefficient for breast tumor detection in microwave tomography. Open J. Antennas Propag. 3(December), 27–36 (2015)

    CrossRef  Google Scholar 

  4. Shea, J.D., Kosmas, P., Van Veen, B.D., Hagness, S.C.: Contrast-enhanced microwave imaging of breast tumors: a computational study using 3D realistic numerical phantoms. Inverse Probl. 26(74009), 1–22 (2010)

    MathSciNet  MATH  Google Scholar 

  5. Shea, J.D., Kosmas, P., Hagness, S.C., Van Veen, B.D.: Three-dimensional microwave imaging of realistic numerical breast phantoms via a multiple-frequency inverse scattering technique. Med. Phys. 37(8), 4210–4226 (2010)

    CrossRef  Google Scholar 

  6. Winters, D.W., Van Veen, B.D., Hagness, S.C.: A sparsity regularization approach to the electromagnetic inverse scattering problem. IEEE Trans. Antennas Propag. 58(1), 145–154 (2010)

    CrossRef  MathSciNet  Google Scholar 

  7. Joachimowicz, N., Pichot, C., Hugonin, J.-P.: Inverse Scattering: an iterative numerical method for electromagnetic imaging. IEEE Trans. Antennas Propag. 39(12), 1742–1752 (1991)

    CrossRef  Google Scholar 

  8. Hansen, P.C., O’Leary, D.P.: The use of the L-curve in the regularization of discrete Ill-Posed problems. SIAM J. Sci. Comput. 14(6), 1487–1503 (1993)

    CrossRef  MathSciNet  Google Scholar 

  9. Hansen, P.C.: Regularization Tools—A Matlab Package for Analysis and Solution of Discrete Ill-Posed Problems (2008)

    Google Scholar 

  10. van der Vorst, H.A.: BI-CGSTAB: a fast and smoothly converging variant of Bi-Cg for the solution of nonsymmetric linear systems*. SIAM J. Sci. Stat. Comput. 13(2), 631–644 (1992)

    CrossRef  MathSciNet  Google Scholar 

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Correspondence to Latifah Mohamed .

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Mohamed, L., Affendi, N.A.M., Ali, A., Abdullah, N. (2019). Microwave Tomography: A Numerical Study of Solving Linear Equations in the Non-linear Inverse Scattering Problem. In: Kor, LK., Ahmad, AR., Idrus, Z., Mansor, K. (eds) Proceedings of the Third International Conference on Computing, Mathematics and Statistics (iCMS2017). Springer, Singapore.

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