Alleviating Global Multiple Scattering Effects in Electromagnetic Inverse Scattering Problems using CIE-I

This article examines the challenges of accurately estimating contrast in electromagnetic inverse scattering problems (ISPs) when dealing with strong scatterers. The nonlinearity inherent in these problems stems primarily from multiple scattering effects, which are represented by a global-effect term '(A(Ij))' in the least squares method used to solve for the unknown contrast R after updating the induced current.

For weak or not-too-strong scatterers, the global-effect term's contribution is minor compared to the incident field. This allows for accurate contrast estimation, guiding the inversion towards the global solution. However, strong scatterers make the global-effect term significant, influencing the entire domain through the global Green's operator 'A'. Due to the lack of information about the induced current 'Ij' at the inversion's outset, contrast estimation becomes less accurate and further from the global minimum.

To address this, the article proposes a strategy of gradually decreasing the regularized parameter 'β' within the nested inversion. This effectively suppresses the global effect caused by the '(A(Ij))' term. Initially, large 'β' values ensure the modified local-effect term dominates over the global-effect term, enabling accurate contrast estimation. As the inversion progresses, gradually reducing 'β' allows for the gradual introduction of the global effect, leading to a more precise contrast estimation.

This approach, known as the Conjugate-Gradient Iterative Eshelby (CIE-I) method, effectively reduces the influence of global multiple scattering on contrast estimation in CSI-type methods. For a deeper understanding of this approach, readers are encouraged to refer to reference [30].