Scattering coefficients of inhomogeneous objects and their application in target classification in wave imaging. (English) Zbl 1505.65288
Summary: The aim of this paper is to provide and numerically test in the presence of measurement noise a procedure for target classification in wave imaging based on comparing frequency-dependent distribution descriptors with precomputed ones in a dictionary of learned distributions. Distribution descriptors for inhomogeneous objects are obtained from the scattering coefficients. First, we extract the scattering coefficients of the (inhomogeneous) target from the perturbation of the reflected waves. Then, for a collection of inhomogeneous targets, we build a frequency-dependent dictionary of distribution descriptors and use a matching algorithm in order to identify a target from the dictionary up to some translation, rotation and scaling.
MSC:
| 65N21 | Numerical methods for inverse problems for boundary value problems involving PDEs |
| 35B30 | Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs |
| 35C20 | Asymptotic expansions of solutions to PDEs |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
| 78A46 | Inverse problems (including inverse scattering) in optics and electromagnetic theory |
| 78M50 | Optimization problems in optics and electromagnetic theory |
| 35R30 | Inverse problems for PDEs |
Keywords:
target classification; inhomogeneous inclusions; scattering coefficients; frequency-dependent distribution descriptors; far-field measurementsReferences:
| [1] | Abbas, T., Ammari, H., Hu, G., Wahab, A. & Ye, J.Ch. (2017) Elastic scattering coefficients and enhancement of nearly elastic cloaking. J. Elast.128, 203-243. · Zbl 1374.74053 |
| [2] | Abramowitz, M. & Stegun, I. (1964) Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards Applied Mathematics Series, Vol. 55, Dover, New York. · Zbl 0171.38503 |
| [3] | Ammari, H., Boulier, T. & Garnier, J. (2014) Shape recognition and classification in electro-sensing. Proceedings of the National Academy of Sciences USA111, 11652-11657. · Zbl 1355.92056 |
| [4] | Ammari, H., Boulier, T., Garnier, J., Jing, W., Kang, H. & Wang, H. (2014) Target identification using dictionary matching of generalized polarization tensors. Found. Comput. Math.14, 27-62. · Zbl 1294.94006 |
| [5] | Ammari, H., Chow, Y. T. & Zou, J. (2014) The concept of heterogeneous scattering coefficients and its application in inverse medium scattering. SIAM J. Math. Anal.46, 2905-2935. · Zbl 1301.35073 |
| [6] | Ammari, H., Chow, Y. T. & Zou, J. (2014) The concept of heterogeneous scattering coefficients and its application in inverse medium scattering, preprint, arXiv:1310.6096, 2013. · Zbl 1301.35073 |
| [7] | Ammari, H., Chow, Y. T. & Zou, J. (2016) Phased and phaseless domain reconstruction in inverse scattering problem via scattering coefficients. SIAM J. Appl. Math.76, 1000-1030. · Zbl 1338.35490 |
| [8] | Ammari, H., Chow, Y. T. & Zou, J. (2018) Super-resolution in imaging high contrast targets from the perspective of scattering coefficients. J. Math. Pures Appl.111, 191-226. · Zbl 1391.35408 |
| [9] | Ammari, H., Deng, Y., Kang, H. & Lee, H. (2014) Reconstruction of inhomogeneous conductivities via generalized polarization tensors. Ann. IHP Anal. Non Lin.31, 877-897. · Zbl 1298.35247 |
| [10] | Ammari, H., Garnier, J., Jing, W., Kang, H., Lim, M., Sølna, M. & Wang, G. (2013) Mathematical and Statistical Methods for Multistatic Imaging, Springer, Cham, Switzerland. · Zbl 1288.35001 |
| [11] | Ammari, H. & Kang, H. (2004) Boundary layer techniques for solving the Helmholtz equation in the presence of small inhomogeneities. J. Math. Anal. Appl.296, 190-208. · Zbl 1149.35337 |
| [12] | Ammari, H., Kang& H., Lee (2009) Layer potential techniques in spectral analysis, Mathematical Surveys and Monographs, vol. 153, American Mathematical Society, Providence, RI. MR2488135 · Zbl 1167.47001 |
| [13] | Ammari, H., Kang, H., Lee, H. & Lim, M. (2013) Enhancement of Near-Cloaking. Part II: The Helmholtz Equation. Comm. Math. Phys.317, 485-502. · Zbl 1260.35095 |
| [14] | Ammari, H., Garnier, J., Jugnon, V., Lee, H. & Lim, M. (2012) Enhancement of near-cloaking. Part III: Numerical simulations, statistical stability, and related questions. In: Multi-scale and High-Contrast PDE: from Modelling, to Mathematical Analysis, to Inversion, Contemp. Math., Vol. 577, Amer. Math. Soc., Providence, RI, pp. 1-24. · Zbl 1303.35107 |
| [15] | Ammari, H., Tran, M. P. & Wang, H. (2014) Shape identification and classification in echolocation. SIAM J. Imaging Sci.7, 1883-1905. · Zbl 1309.65128 |
| [16] | Ammari, H., Kang, H., Kim, E. & Lee, J.-Y. (2012) The generalized polarization tensors for resolved imaging. Part II: Shape and electromagnetic parameters reconstruction of an electromagnetic inclusion from multistatic measurements. Math. Comp.81, 839-860. · Zbl 1251.49053 |
| [17] | Ammari, H., Fitzpatrick, B., Kang, H., Ruiz, M., Yu, S. & Zhang, H. (2018) Mathematical and computational methods in photonics and phononics, Mathematical Surveys and Monographs, Vol. 235, Amer, Math. Soc., Providence. · Zbl 1420.78001 |
| [18] | Colton, D. & Kress, R. (1992) Inverse Acoustic and Electromagnetic Scattering Theory. Applied Math. Sciences, Vol. 93, Springer-Verlag, New York. · Zbl 0760.35053 |
| [19] | Kleeman, L. & Kuc, R. (1995) Mobile robot sonar for target localization and classification. Internat. J. Robotics Res.14, 295-318. |
| [20] | Nédélec, J. C. (1992) Quelques propriétés des dérivées logarithmiques des fonctions de Hankel. C. R. Acad. Sci. Paris, Série I314, 507-510. · Zbl 0747.34020 |
| [21] | Pólya, G. & Szegö, G. (1951) Isoperimetric Inequalities in Mathematical Physics, Ann. Math. Stud. Vol. 27, Princeton University Press, Princeton, NJ. · Zbl 0044.38301 |
| [22] | Simmons, J. A. (1979) Perception of echo phase information in bat sonar. Science204, 1336-1338. |
| [23] | Simmons, J. A., Fenton, M. B. & O’Farrell, M. J. (1979) Echolocation and pursuit of prey by bats. Science203, 16-21. |
| [24] | Wang, H. (2014) Shape identification in electro-sensing, https://github.com/yanncalec/SIES |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
