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 ℓ₁-norm constraints of the wavelet coefficients, a least absolute shrinkage and selection operator (LASSO) problem that searches for the global minimum of the ℓ₂-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.
An Approximation of 2-D Inverse Scattering Problems From a Convex Optimization Perspective
Soldovieri F;
2021
Abstract
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 ℓ₁-norm constraints of the wavelet coefficients, a least absolute shrinkage and selection operator (LASSO) problem that searches for the global minimum of the ℓ₂-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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.