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| We consider inverse medium scattering problem where the aim is to reconstruct a spatially dependent index of refraction form field measurements of waves scattered in a inhomogeneous medium.
In particular we discuss the case, that the medium is sparse with respect to some a-priori known basis. Such inversion problems can be reformulated using Tikhonov-like functionals with $L^p$ or $\ell^p$ penalty terms.
In the talk we first discuss continuity and differentiability properties of the forward problem, then the implications for the reconstruction scheme and finally we present numerical results. |
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