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An Approximation of 2-D Inverse Scattering Problems From a Convex Optimization Perspective

journal contribution
posted on 22.07.2022, 18:42 authored by Yangqing Liu, Shuo HanShuo Han, Francesco Soldovieri, Danilo ErricoloDanilo Erricolo
We present a two-step strategy to solve an inverse scattering problem in 2-D geometry. The first step approximates the inverse scattering as a convex optimization problem and provides an estimation of the total field inside the domain under investigation without a priori knowledge or tuning parameters. In the second step, the previously estimated total field is used to reconstruct the unknown contrast permittivity, which is represented by a superposition of level-1 Haar wavelet transform basis functions. Subject to {\ell -{1}} -norm constraints of the wavelet coefficients, a least absolute shrinkage and selection operator (LASSO) problem that searches for the global minimum of the {\ell -{2}} -norm residual is exploited by accounting for the sparsity of the wavelet-based permittivity representation. Numerical results are presented to assess the effectiveness of the proposed formulation against objects with relatively small electric size. Finally, the approach is validated against experimental data.

History

Citation

Liu, Y., Han, S., Soldovieri, F.Erricolo, D. (2021). An Approximation of 2-D Inverse Scattering Problems From a Convex Optimization Perspective. IEEE Geoscience and Remote Sensing Letters, 19, 1-5. https://doi.org/10.1109/lgrs.2021.3079885

Publisher

Institute of Electrical and Electronics Engineers (IEEE)

issn

1545-598X