Well-posed microwave imaging in focusing media: 2D generalization and impact on convergence of the contrast source inversion method

Abstract

The imaging experiments of microwave tomography are typically conducted in free space or other types of environment lacking focusing properties. Such experiments lead to inherent ill-posedness of the underlying inverse problem. This ill-posedness dramatically complicates reconstruction of the sought object properties from the collected information about its scattered field. In our recent work (Okhmatovski, et.al., IEEE TAP, vol. 60, no. 5, pp. 2418–2430, 2012) we showed that the ill-posedness of the inverse problem is not inherent, however, but rather originates from improperly staged imaging experiments. If the medium in which imaging experiment is conducted features focusing properties and the field scattered by the object is collected at properly prescribed locations the ill-posedness of the imaging experiment can be eliminated. Examples of such focusing media formed by Veselago Lens, Maxwell Fish Eye Lens, and parabolic mirror have been previously shown to allow for direct reconstruction of 1D objects. In this work we demonstrate numerical experiments in which the Veselago Lens is utilized for direct non-regularized reconstruction of 2D objects. We also study the impact of media in which imaging experiment is staged on the convergence Contrast Source Inversion (CSI) iterative algorithm for solution of the inverse problem.