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

• Published in: IEEE geoscience and remote sensing letters Vol. 19; pp. 1 - 5
• Main Authors: Liu, Yangqing, Han, Shuo, Soldovieri, Francesco, Erricolo, Danilo
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Approximation; Basis functions; Coefficients; Convex analysis; Convex functions; Convex optimization; Convexity; CVX; Electromagnetic scattering; Haar transform; Inverse problems; Inverse scattering; least absolute shrinkage and selection operator (LASSO); Operators (mathematics); Optimization; Permittivity; radar imaging; templates for first-order conic solver (TFOCS); Wavelet domain; Wavelet transforms
• ISSN: 1545-598X; 1558-0571
• DOI: 10.1109/LGRS.2021.3079885

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 <inline-formula> <tex-math notation="LaTeX">{\ell _{1}} </tex-math></inline-formula>-norm constraints of the wavelet coefficients, a least absolute shrinkage and selection operator (LASSO) problem that searches for the global minimum of the <inline-formula> <tex-math notation="LaTeX">{\ell _{2}} </tex-math></inline-formula>-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.