New Model based Methods

A smart and suitable rewriting of the Lippman Schwinger basic equation can allow for a reduction of the ‘degree of non-linearity’ of the inverse scattering problem and hence advantages in term of convergence and accuracy of the related inversion procedures. Accordingly, new scattering models can be derived in a number of cases. For instance, in [1]-[7] a new model, called CS-EB, is derived by exploiting the Green’s function peaked behaviour in the presence of losses in the background medium and tested against different scenarios, which include both 3D geometry and experimental data. On the other hand, [8] introduce the Y0 model, which is based on a convenient decomposition of the pertaining Green’s function, which allows to extract the main contribution of the radiating currents to the total field. Finally, in [9] three different rewritings are discussed and compared by emphasizing similarities and differences. Moreover, also in [9], in the same ‘rewriting’ spirit, the ‘Virtual Experiments’ framework is re-interpreted and exploited in order to give rise to new hybrid inversion methods.

1. T. Isernia, L. Crocco and M. D’Urso, “New tools and series for forward and inverse scattering problems in lossy media,”  IEEE Geoscience and Remote Sensing Letters, vol. 1, no. 4, pp. 327-331, 2004. [click here] 
2. L. Crocco, M. D’Urso, and T. Isernia, “Testing the contrast source extended Born inversion method against real data: the TM case,” Inverse Problems, vol. 21, no. 6, 2005. [click here]
3. I. Catapano, L. Crocco, M. D’Urso and T. Isernia, “A novel effective model for solving 3-D nonlinear inverse scattering problems in lossy scenarios,” IEEE Geoscience and Remote Sensing Letters, vol. 3, no. 3, pp. 302-306, 2006. [click here]
4. I. Catapano, L. Crocco, M. D’Urso, and T. Isernia, “On the Effect of Support Estimation and of a New Model in 2-D Inverse Scattering Problems,” IEEE Transaction on Antennas and Propagation, vol. 55, no. 6, pp.1895-1899, 2007. [click here]
5. M. D’Urso, I. Catapano, L. Crocco and T. Isernia, “Effective Solution of 3-D Scattering Problems via Series Expansions: Applicability and a New Hybrid Scheme,” IEEE Transactions on Geoscience and Remote Sensing, vol. 45, no. 3, pp. 639-648, 2007. [click here]
6. I. Catapano, L. Crocco, M. D’Urso, and T. Isernia, “3D microwave imaging via preliminary support reconstruction: Testing on the Fresnel 2008 database,” Inverse Problems, vol. 25, no. 2, 2009. [click here] 
7. M. D’Urso, T. Isernia and A. F. Morabito, “On the Solution of 2-D Inverse Scattering Problems via Source-Type Integral Equations,” IEEE Transactions on Geoscience and Remote Sensing, vol. 48, no. 3, pp. 1186-1198, 2010. [click here]
8. M. T. Bevacqua and T. Isernia, “An Effective Rewriting of the Inverse Scattering Equations via Green’s Function Decomposition,” IEEE Transactions on Antennas and Propagation, 2021 (in press). 
9. M. T. Bevacqua and T. Isernia, “Quantitative Non-Linear Inverse Scattering: a Wealth of Possibilities Through Smart Rewritings of the Basic Equations,” arXiv:2012.15252, 2020 (arXiv preprint). [click here]