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This paper proposes an iterative technique to reconstruct the source term in transport equations, which account for scattering effects, from boundary measurements. In the two-dimensional setting, the full outgoing distribution in the phase space (position and direction) needs to be measured. In three space dimensions, we show that measurements for angles… (More)

We consider the problem of recovering a sufficiently smooth isotropic conductivity from interior knowledge of the magnitude of the current density field |J| generated by an imposed voltage potential f on the boundary. In any dimension n ≥ 2, we show that equipotential sets are global area minimizers in the conformal metric determined by |J|. In two… (More)

We consider the problem of recovering an isotropic conductivity outside some perfectly conducting or insulating inclusions from the interior measurement of the magnitude of one current density field |J|. We prove that the conductivity outside the inclusions, and the shape and position of the perfectly conducting and insulating inclusions are uniquely… (More)

We characterize the range of the attenuated and non-attenuated X-ray transform of compactly supported vector fields in the plane. The characterization is in terms of a Hilbert transform associated with the A-analytic functionsà la Bukhgeim. As an application we determine necessary and sufficient conditions for the attenuated Doppler and X-ray data to be… (More)

Recent research in electrical impedance tomography produce images of biological tissue from frequency differential boundary voltages and corresponding currents. Physically one is to recover the electrical conductivity σ and permittivity ϵ from the frequency differential boundary data. Let γ = σ +iωϵ denote the complex admittivity, Λγ be the corresponding… (More)

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