Vincent Mouysset | Searcharxiv

arXiv2013

Adaptive refinement and selection process through defect localization for reconstructing an inhomogeneous refraction index

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.

math.NA↗

arXiv2013

An optimization approach for the localization of defects in an inhomogeneous medium from acoustic far-field measurements at a fixed frequency

We are interested in the localization of defects in non-absorbing inhomogeneous media with far-field 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.

math.NA↗