Complex geometrical optics solutions for anisotropic equations and applications

Takuwa, Hideki; Uhlmann, Günther; Wang, Jenn‐Nan

doi:10.1515/jiip.2008.049

Cited by 6 publications

(1 citation statement)

References 22 publications

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“…For the anisotropic case in the three-dimensions, one can use the oscillating-decaying solutions to reconstruct unknown obstacles in a given medium, see [34,35,42,43]. It is worth mentioning that for the anisotropic case in the plane, one can also construct CGOs via the quasi-conformal map, and we refer readers to [48] for more detailed discussions.…”

Section: Introductionmentioning

confidence: 99%

A direct reconstruction algorithm for the anisotropic inverse conductivity problem based on Calderón’s method in the plane

et al. 2020

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A direct reconstruction algorithm based on Calderón's linearization method for the reconstruction of isotropic conductivities is proposed for anisotropic conductivities in two-dimensions. To overcome the non-uniqueness of the anisotropic inverse conductivity problem, the entries of the unperturbed anisotropic tensors are assumed known a priori, and it remains to reconstruct the multiplicative scalar field. The quasi-conformal map in the plane facilitates the Calderón-based approach for anisotropic conductivities. The method is demonstrated on discontinuous radially symmetric conductivities of high and low contrast.

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Section: Introductionmentioning

confidence: 99%

A direct reconstruction algorithm for the anisotropic inverse conductivity problem based on Calderón’s method in the plane

et al. 2020

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Electrical impedance tomography and Calderón's problem

2009

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We survey mathematical developments in the inverse method of Electrical Impedance Tomography which consists in determining the electrical properties of a medium by making voltage and current measurements at the boundary of the medium. In the mathematical literature this is also known as Calderón's problem from Calderón's pioneer contribution [23]. We concentrate this article around the topic of complex geometrical optics solutions that have led to many advances in the field. In the last section we review some counterexamples to Calderón's problems that have attracted a lot of interest because of connections with cloaking and invisibility.

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Reconstruction of penetrable obstacles in the anisotropic acoustic scattering

Lin¹

2016

IPI

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Complex geometrical optics solutions for anisotropic equations and applications

Cited by 6 publications

References 22 publications

A direct reconstruction algorithm for the anisotropic inverse conductivity problem based on Calderón’s method in the plane

A direct reconstruction algorithm for the anisotropic inverse conductivity problem based on Calderón’s method in the plane

Electrical impedance tomography and Calderón's problem

Reconstruction of penetrable obstacles in the anisotropic acoustic scattering

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