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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)
The inverse scattering for an obstacle D ⊂ R2 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 distance between the given far field information g∞(More)
In this paper, we deal with the inverse spectral problem for the equation −(pu′)′ +qu = λru on a finite interval (0, h). The above equation subjected to appropriate boundary conditions on zero and h gives the vibrations of a string of length h. Using the Dirichlet-to-Neumann map type approach known in the multidimensional Calderón problem, we prove some(More)
In this article, we use the no-response test idea, introduced in Luke and Potthast (2003) and Potthast (Preprint) and the inverse obstacle problem, to identify the interface of the discontinuity of the coefficient of the equation · x + c x with piecewise regular and bounded function c x . We use infinitely many Cauchy data as measurement and give a(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 goal of this work is to investigate the relation of the no-response approach to some other non-iterative reconstruction schemes. We will derive several equivalence statements and dependency results. For simplicity we consider the obstacle reconstruction problem from far field data. In particular, we investigate two versions of the no-response test (NRT)(More)
In this paper, we investigate the problem of reconstructing sound-soft acoustic obstacles using multifrequency far field measurements corresponding to one direction of incidence. The idea is to obtain a rough estimate of the obstacle’s shape at the lowest frequency using the least-squares approach, then refine it using a recursive linearization algorithm at(More)