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IPI

Consider the scattering of the two-or three-dimensional Helmholtz equation where the source of the electric current density is assumed to be compactly supported in a ball. This paper concerns the stability analysis of the inverse source scattering problem which is to reconstruct the source function. Our results show that increasing stability can be obtained for the inverse problem by using only the Dirichlet boundary data with multi-frequencies.

IPI

A novel method is developed for solving the inverse obstacle scattering
problem in near-field imaging. The obstacle surface is assumed to be a small and
smooth deformation of a circle. Using the transformed field expansion, the
direct obstacle scattering problem is reduced to a successive sequence of
two-point boundary value problems. Analytical solutions of these problems are
derived by a Green's function method. The nonlinear inverse problem is
linearized by dropping the higher order terms in the power series expansion.
Based on the linear model and analytical solutions, an explicit reconstruction
formula is obtained. In addition, a nonlinear correction scheme is devised to
improve the results dramatically when the deformation is large. The method
requires only a single incident wave at a fixed frequency. Numerical tests show
that the method is stable and effective for near-field imaging of
obstacles with subwavelength resolution.

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