Reconstruction of Small Inhomogeneities from Boundary Measurements

By Habib M. Ammari, Hyeonbae Kang. 2005

645 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/6e21d68c323b9a4aba9bd38e549bc7c3ce8fed13

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In Computational Theory and Mathematics

Citations in the corpus

Acoustic inverse scattering using topological derivative of far-field measurements-based L2 cost functionals (2013, neutral): “– Use of the MUSIC algorithm to deal with inverse scattering problems [13, 14].”
Inverse problems in elasticity (2005, methodology): “Also relevant is the systematic method for deriving asymptotic expansions of the relevant field variable, and its application to the identification of small inhomogeneities, proposed in [2, 4, 5].”
Level set methods for inverse scattering (2006, background): “Let us also signal the encompassing asymptotic framework of electromagnetic and elastic fields involving the so-called generalized polarization tensors developed in [8] which (even if topological derivatives and higher orders are not introduced per se by the authors) gives us very powerful tools to ”
On the Spectrum of the Poincaré Variational Problem for Two Close-to-Touching Inclusions in 2D (2013, background): “The following result can be found in [3] for connected domains.”
Minimum stress optimal design with the level set method. (2008, background): “The same idea has also been proposed independently in the context of inverse problems by Ammari and his co-workers [8], [9], [10].”
A study on orthogonality sampling (2010, background): “For further literature about the reconstruction of small objects we refer to [1] and the rich body of the literature cited there.”
A method of biological tissues elasticity reconstruction using magnetic resonance elastography measurements (2007, methodology): “See also the book [3] and its list of references.”
A new algorithm for topology optimization using a level-set method (2006, methodology): “By using the expression of the elastic moment tensor calculated in [7], the following functions have been obtained in linear elasticity 2D plane strain: The constants λ and µ are the Lam´e coeﬃcients and the stress tensor σ ( u Ω ) is computed with the local density at the point x .”