A Qualitative Two-Step Inversion Approach for the Reconstruction of Subsurface Defects

Donelli, Massimo and Benedetti, Manuel and Lesselier, D. and Massa, Andrea (2011) A Qualitative Two-Step Inversion Approach for the Reconstruction of Subsurface Defects. [Technical Report]

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Abstract

The detection of subsurface objects such as landmine or archaeological find, the location of sedimentary layer for geological inspections, or the identification of cracks and voids in host structures are some examples of applications where the reconstruction of the position and the shape of unknown targets embedded in inaccessible regions is required. In this framework, the imaging methods based on electromagnetic inverse scattering theory can play a key role [1]. As a matter of fact, the electromagnetic and geometric properties of the region under test can be quantitatively reconstructed starting from the observation of the scattered field. Unfortunately, the problem at hand presents several drawbacks such as non-linearity and ill-posedness that need to be taken into account especially when dealing with complex scenarios. However, a considerable amount of a-priori information is generally available in nondestructive testing and evaluation (NDT/NDE) applications, since the crack to be reconstructed is located in a known host medium [2]. Such a peculiarity can be profitably exploited in order to cope with the lack of information characterizing the inverse problem. In such a framework, microwave methodologies based on the use of heuristic optimizers and on the exploitation of the a-priori information have been effectively used for the detection of a crack in a known host structure [3] or when dealing with more complex and realistic scenarios characterized by multiple defects [4]. The proposed approaches demonstrate their feasibility and effectiveness in providing a coarse estimation of the targets in a qualitative fashion, but they are not suitable for the retrieval of complex shapes. In this work, a two-step procedure successfully adopted for NDT/NDE problems [5] has been employed for the qualitative reconstruction of complex subsurface targets. In particular, at the first step the target is localized and its shape is roughly estimated starting from the knowledge of the scattered field. Then, the second step is aimed at refining the contour of the target by means of a shape optimization technique characterized by the evolution of a level set function [6].

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