The reciprocity gap method for a cavity in an inhomogeneous medium
Fang Zeng Xiaodong Liu Jiguang Sun Liwei Xu
Inverse Problems & Imaging 2016, 10(3): 855-868 doi: 10.3934/ipi.2016024
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.
keywords: inhomogeneous medium reciprocity gap method. Interior inverse scattering problem
Inverse scattering using finite elements and gap reciprocity
Peter Monk Jiguang Sun
Inverse Problems & Imaging 2007, 1(4): 643-660 doi: 10.3934/ipi.2007.1.643
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.
keywords: Finite Elements. Gap Reciprocity Inverse Scattering
A decomposition method for an interior inverse scattering problem
Fang Zeng Pablo Suarez Jiguang Sun
Inverse Problems & Imaging 2013, 7(1): 291-303 doi: 10.3934/ipi.2013.7.291
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.
keywords: Interior inverse scattering problem decomposition method Helmholtz equations.

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