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In this paper, we are concerned with the identification of complex obstacles from the scattering data for the acoustic problem. The complex obstacle is characterized by its shape and the boundary values of the impedance coefficient. We establish pointwise formulas which can be used to reconstruct the shape of the obstacle and give explicitly the values of… (More)

Magnetic resonance electrical impedance tomography (MREIT) is a new medical imaging technique that aims to provide electrical conductivity images with sufficiently high spatial resolution and accuracy. A new MREIT image reconstruction method called the harmonic Bz algorithm was proposed in 2002, and it is based on the measurement of Bz that is a single… (More)

The inverse scattering for an obstacle D ⊂ R 2 with mixed boundary condition can be considered as a prototype for radar detection of complex obstacles with coated and noncoated parts of the boundary. We construct some indicator functions for this inverse problem using the far-field pattern directly, without the necessity of transforming the far field to the… (More)

We consider the reconstruction of complex obstacles from few farfield acoustic measurements. The complex obstacle is characterized by its shape and an impedance function distributed along its boundary through Robin type boundary conditions. This is done by minimizing an objective functional, which is the L 2 distance between the given far field information… (More)

This paper concerns the acoustic scattering by an extended obstacle surrounded by point-like obstacles. The extended obstacle is supposed to be rigid, while the point-like obstacles are modeled by point perturbations of the exterior Laplacian. In the first part, we consider the forward problem. Following two equivalent approaches (the Foldy formal method… (More)

In this work, we are concerned with the inverse scattering by interfaces for the linearized and isotropic elastic model at a fixed frequency. First, we derive complex geometrical optic solutions with linear or spherical phases having a computable dominant part and an H α-decaying remainder term with α < 3, where H α is the classical Sobolev space. Second,… (More)

In this paper, we are concerned with the detection of point-like obstacles using elastic waves. We show that one type of waves, either the P or the S scattered waves, is enough for localizing the points. We also show how the use of S incident waves gives better resolution than the P waves. These affirmations are demonstrated by several numerical examples… (More)