Let q(x) be real-valued compactly supported sufficiently smooth function. It is proved that the scattering data A(−β, β, k) ∀β ∈ S, ∀k > 0 determine q uniquely. MSC: 35P25, 35R30, 81Q05; PACS: 03.65.Nk

Optical coherence tomography is a non-invasive imaging technique based on the use of light sources exhibiting a low degree of coherence. Low-coherence interferometric microscopes have been successful in producing internal images of thin pieces of biological tissue; typically samples of the order of 1 mm in depth have been imaged, with a resolution of the order of 10 μm in some portions of the s...

We consider the image reconstruction problem for optical tomography with diffuse light. The associated inverse scattering problem is analyzed by making use of particular symmetries of the scattering data. The effects of sampling and limited data are analyzed for several different experimental modalities, and computationally efficient reconstruction algorithms are obtained. These algorithms are ...

Uniqueness in inverse conductivity and scattering problems is considered. In case the medium consists of two discontinuous constant anisotropic conductive parts, the measurements of potential and induced currents on the boundary of surrounding body are enough to guarantee uniqueness to determine conductivity and region of embedded unknown material under a very weak condition. The analogous uniq...

We solve the inverse scattering problem for multidimensional vector fields and we use this result to construct the formal solution of the Cauchy problem for the second heavenly equation of Plebanski, a scalar nonlinear partial differential equation in four dimensions relevant in General Relativity, which arises from the commutation of multidimensional Hamiltonian vector fields.

It is proved that if the scattering amplitudes for two obstacles (from a large class of obstacles) differ a little, then the obstacles differ a little, and the rate of convergence is given. An analytical formula for calculating the characteristic function of the obstacle is obtained, given the scattering amplitude at a fixed frequency.

It is proved that the scattering amplitude known at a fixed frequency, a fixed direction of the incident plane wave and all directions of the scattered wave in a solid angle, however small, determine uniquely the shape of a strictly convex obstacle with a smooth but not analytic boundary on which the Dirichlet boundary condition is assumed.

We use the linear sampling method to determine the shape and surface conductivity of a partially coated dielectric infinite cylinder from a knowledge of the far field pattern of the scattered TM polarized electromagnetic wave at fixed frequency. A mathematical justification of the method is provided based on the use of a complete family of solutions. Numerical examples are given showing the eff...

We prove new global Hölder-logarithmic stability estimates for the near-field inverse scattering problem in dimension d ≥ 3. Our estimates are given in uniform norm for coefficient difference and related stability efficiently increases with increasing energy and/or coefficient regularity. In addition, a global logarithmic stability estimate for this inverse problem in dimension d = 2 is also gi...

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