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We characterize the non-uniqueness in the inverse problem for the stationary transport model, in which the absorption a and the scattering coefficient k of the media are to be recovered from the albedo operator. We show that " gauge equivalent " pairs (a, k) yield the same albedo operator, and that we can recover uniquely the class of the gauge equivalent… (More)
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 present new necessary and sufficient conditions for a function on ∂Ω×S 1 to be in the range of the attenuated Radon transform of a sufficiently smooth function support in the convex set Ω ⊂ R 2. The approach is based on an explicit Hilbert transform associated with traces on the boundary of A-analytic functions in the sense of Bukhgeim.
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 study the inverse conductivity problem of how to reconstruct an isotropic electrical conductivity distribution γ in an object from static electrical measurements on the boundary of the object. We give an exact reconstruction algorithm for the conductivity γ ∈ C 1+ǫ (Ω) in the plane domain Ω from the associated Dirichlet to Neumann map on ∂Ω. Hence we… (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)
In this paper we reconstruct convection coefficients from boundary measurements. We reduce the Beals and Coifman formalism from a linear first order system to a formalism for the ∂-equation.
In this paper we study the attenuated X-ray transform of 2-tensors supported in strictly convex bounded subsets in the Euclidean plane. We characterize its range and reconstruct all possible 2-tensors yielding identical X-ray data. The characterization is in terms of a Hilbert-transform associated with A-analytic maps in the sense of Bukhgeim.
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)