## Journals

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### Open Access Journals

IPI

We consider an interior inverse medium problem of reconstructing the shape of a cavity. Both the measurement locations and point sources are inside the cavity.
Due to the lack of a priori knowledge of physical prosperities of the medium inside the cavity and to avoid the computation of background Green's functions, the reciprocity gap method is employed. We prove the related theory and present some numerical examples for validation.

IPI

In this paper we consider the inverse scattering problem of
determining the shape of one or more objects embedded in an
inhomogeneous background from Cauchy data measured on the boundary
of a domain containing the objects in its interior. Following
[1], we use the reciprocity gap functional method. In an
inhomogeneous background medium the use of a Herglotz wave function
in the reciprocity gap functional is no longer permissable. Instead
we propose to use a finite element representation. We provide
analysis to support the method, and also describe implementation
issues. Numerical examples are given showing the performance of the
method.

IPI

We consider an interior inverse scattering problem of reconstructing the shape of a cavity.
The measurements are the scattered fields on a curve inside the cavity due to one point source.
We employ the decomposition method to reconstruct the cavity and present some convergence results.
Numerical examples are provided to show the viability of the method.

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