Improving the Reconstruction Accuracy of Inversion Strategies Through Energetic Constraints

Franceschini, Davide and Benedetti, Manuel and Viani, Federico and Massa, Andrea (2011) Improving the Reconstruction Accuracy of Inversion Strategies Through Energetic Constraints. [Technical Report]

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Abstract

Microwave imaging techniques are widely investigated in many applied sciences such as the subsurface prospecting [1] and the medical diagnosis [2]. Unfortunately, when inverse scattering approaches are considered, the drawbacks of non-linearity and ill-posedness [3] have unavoidably to be dealt with. Therefore, the problem at hand is usually recast as the minimization of a suitable cost function to be properly minimized in order to find the optimal solution. Such a cost function is usually defined by two discrepancy terms based on the knowledge of the scattered field measured in a suitable observation region and of the incident field in the investigation region. Moreover, further regularization terms have been studied and successfully applied in order to enhance the quality of the reconstructions (e.g., [4][5]). In such a framework, this contribution presents a new constraint based on the conservation of energy to improve the reconstruction accuracy of inverse scattering procedures.

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