Solving Multi‐Resolution Quantitative Inverse Scattering Problems Through the IMSA‐NIE Method

SALUCCI, Marco and POLO, Alessandro and MASSA, Andrea Solving Multi‐Resolution Quantitative Inverse Scattering Problems Through the IMSA‐NIE Method. Technical Report. ELEDIA@UniTN (DISI - University of Trento).

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Abstract

The Iterative Multi‐Scaling Approach (IMSA) is a well‐known recipe to counteract the non‐linearity and ill‐posedness of an inverse scattering (IS) problem. As a matter of fact, it allows to keep as low as possible the ratio between problem unknowns and non‐redundant/informative data. In this way, the occurrence of local minima (i.e., false solutions of the IS problem) is limited with respect to standard (single‐resolution) approaches. Moreover, it exploits progressively‐acquired information on the unknown targets, acting de facto as an effective regularization tool. In this work, the IMSA is integrated with a New Integral Equation (NIE) method, with the goal of further mitigating the non‐linearity of the IS problem and enable the robust quantitative imaging of quite string scatterers under non‐negligible levels of noise on processed data. Numerical results are shown to verify the effectiveness of the integrated IMSA‐NIE approach when dealing with the challenging problem of imaging disconnected scatterers with conductivities different from the surrounding medium (i.e., free‐space).

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