This paper presents a new approach to the electromagnetic inverse scattering formulation of the permittivity profile estimation. The proposed approach is particularly effective for the cases where unknown objects are made of a finite number of homogeneous regions. This approach prevents the need for the Born approximation initial guess and updating the internal total electric field iteratively. The solution to the inverse source problem and scattering problem is not unique. To address the non-uniqueness issue, we have defined the non-radiating objective functions. By minimizing this objective function and applying some constraints, we have been able to obtain a unique permittivity profile. The simulation results indicate that the low-contrast and high-contrast permittivity profiles are accurately estimated by the proposed method. The distinguishing feature of the proposed approach is that by including the non-radiating part of the equivalent source, the unknown permittivity profile becomes the solution to a minimization problem, which is much less computationally intensive as compared to existing methods using iterative field calculation over the entire domain, when applied to large (in terms of wavelength) objects. The high performance of the proposed method for noisy measured data has also been verified.
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