Abstract. We consider non-absorbing inhomogeneous media represented by some refraction index. We have developed a method to reconstruct, from far-field measurements, the shape of the areas where the actual index differs from a reference index. Following the principle of the Factorization Method, we present a fast reconstruction algorithm relying on far field measurements and near field values, easily computed from the reference index. Our reconstruction result is illustrated by several numerical test cases.

We consider the iterative reconstruction of both the internal geometry and the values of an inhomogeneous acoustic refraction index through a piecewise constant approximation. In this context, we propose two enhancements intended to reduce the number of parameters to reconstruct, while preserving accuracy. This is achieved through the use of geometrical informations obtained from a previously developed defect localization method. The first enhancement consists in a preliminary selection of relevant parameters, while the second one is an adaptive refinement to enhance precision with a low number of parameters. Each of them is numerically illustrated.

We are interested in the localization of defects in non-absorbing inhomogeneous media with farfield measurements generated by plane waves. In localization problems, most so-called sampling methods are based on a characterization involving point-sources and the range of some implicitly defined operator. We present here a way to deal with this implicit operator by the means of an optimization approach in the lines of the well-known inf criterion for the factorization method.

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