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- A. Tamasan
- 2008

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)

- Guillaume Bal, Alexandru Tamasan
- SIAM J. Math. Analysis
- 2007

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)

- Adrian Nachman, Alexandru Tamasan, Alexandre Timonov
- SIAM Journal of Applied Mathematics
- 2010

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)

- Amir Moradifam, Adrian Nachman, Alexandru Tamasan
- SIAM J. Math. Analysis
- 2012

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)

- Kamran Sadiq, Alexandru Tamasan
- SIAM J. Math. Analysis
- 2015

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.

- Sungwhan Kim, Alexandru Tamasan
- SIAM J. Math. Analysis
- 2013

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)

- Adrian Nachman, Alexandru Tamasan, Johann Veras
- SIAM Journal of Applied Mathematics
- 2016