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Abstract

Several researches have confirmed the possibility of localizing small anomalies via Kirchhoff migration (KM); however, when the background information is unknown, small anomalies cannot be satisfactorily retrieved. This fact can be examined through the simulation results; however, related theoretical result to explain the reason of such phenomenon has not yet been investigated. In this contribution, we show that the imaging function of the KM can be expressed by an infinite series of the Bessel function of the first kind, material properties, and antenna arrangement, and applied alternative value of the background wavenumber. Based on the theoretical result, we explain why the exact location and shape of anomalies cannot be retrieved. The simulation results with synthetic data exhibited to support the theoretical result.

Keywords

Kirchhoff migration scattering matrix background information microwave imaging simulation results

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References

Ammari

and Kang

, Reconstruction of Small Inhomogeneities from Boundary Measurements, Lecture Notes in Mathematics, Vol. 1846, Springer-Verlag, Berlin, 2004.

Aster

R.C.

Borchers

and Thurber

C.H.

, Parameter Estimation and Inverse Problems, 2nd edn, Elsevier, 2013.

Bleistein

Cohen

and Stockwell Jr

J.S.

, Mathematics of Multidimensional Seismic Imaging, Migration, and Inversion, Interdisciplinary Applied Mathematics, Vol. 13, Springer, New York, 2001.

Colton

and Kress

, Inverse Acoustic and Electromagnetic Scattering Problems, Mathematics and Applications Series, Vol. 93, Springer, New York, 1998.

Zhdanov

M.S.

, Geophysical Inverse Theory and Regularization Problems, Elsevier, Amsterdam, The Netherlands, 2002.

Ahn

C.Y.

and Park

W.-K.

, Kirchhoff migration for identifying unknown targets surrounded by random scatterers, Appl. Sci.9 (2019), 4446.

Ammari

Garnier

Kang

Park

W.-K.

and Sølna

, Imaging schemes for perfectly conducting cracks, SIAM J. Appl. Math.71 (2011), 68–91.

Lee

K.-J.

Son

S.-H.

and Park

W.-K.

, A real-time microwave imaging of unknown anomaly with and without diagonal elements of scattering matrix, Results Phys.17 (2020), 103104.

Park

W.-K.

, A novel study on the orthogonality sampling method in microwave imaging without background information, J. Appl. Math. Lett.145 (2023), 108766.

10.

Son

S.-H.

and Park

W.-K.

, Application of the bifocusing method in microwave imaging without background information, J. Korean Soc. Ind. Appl. Math.27 (2023), 109–122.

11.

Haynes

Stang

and Moghaddam

, Real-time microwave imaging of differential temperature for thermal therapy monitoring, IEEE Trans. Biomed. Eng.61 (2014), 1787–1797.

12.

Park

W.-K.

, Real-time microwave imaging of unknown anomalies via scattering matrix, Mech. Syst. Signal Proc.118 (2019), 658–674.

13.

Park

W.-K.

, Application of MUSIC algorithm in real-world microwave imaging of unknown anomalies from scattering matrix, Mech. Syst. Signal Proc.153 (2021), 107501.

14.

Park

W.-K.

Kim

H.P.

Lee

K.-J.

and Son

S.-H.

, MUSIC algorithm for location searching of dielectric anomalies from S-parameters using microwave imaging, J. Comput. Phys.348 (2017), 259–270.

15.

Slaney

Kak

A.C.

and Larsen

L.E.

, Limitations of imaging with first-order diffraction tomography, IEEE Trans. Microwave Theory Tech.32 (1984), 860–874.

16.

Park

W.-K.

, Real-time detection of small anomaly from limited-aperture measurements in real-world microwave imaging, Mech. Syst. Signal Proc.171 (2022), 108937.

Real-time identification of small anomalies from scattering matrix without background information

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