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The problem this paper addresses is how to use the two-dimensional D-bar method for electrical impedance tomography with experimental data collected on finitely many electrodes covering a portion of the boundary of a body. This requires an approximation of the Dirichlet-to-Neumann, or voltage-to-current density map, defined on the entire boundary of the(More)
The problem of reconstructing an unknown electric conductivity from boundary measurements has applications in medical imaging, geophysics, and nondestructive testing. A. Nachman [Ann. of Math. 143 (1996)] proved global uniqueness for the 2-D inverse conductivity problem using a constructive method of proof. Based on this proof, Siltanen, Mueller and(More)
Diagnostic and operational tasks based on dental radiology often require three-dimensional (3-D) information that is not available in a single X-ray projection image. Comprehensive 3-D information about tissues can be obtained by computerized tomography (CT) imaging. However, in dental imaging a conventional CT scan may not be available or practical because(More)
The aim of X-ray tomography is to reconstruct an unknown physical body from a collection of projection images. When the projection images are only available from a limited angle of view, the reconstruction problem is a severely ill-posed inverse problem. Statistical inversion allows stable solution of the limited-angle tomography problem by complementing(More)
A direct (noniterative) reconstruction algorithm for electrical impedance tomography in the two-dimensional (2-D), cross-sectional geometry is reviewed. New results of a reconstruction of a numerically simulated phantom chest are presented. The algorithm is based on the mathematical uniqueness proof by A. I. Nachman [1996] for the 2-D inverse conductivity(More)
A novel approach to the X-ray tomography problem with sparse projection data is proposed. Non-negativity of the X-ray attenuation coefficient is enforced by modelling it as max{Φ(x), 0} where Φ is a smooth function. The function Φ is computed as the equilibrium solution of a nonlinear evolution equation analogous to the equations used in level set methods.(More)
The effects of truncating the (approximate) scattering transform in the D-bar reconstruction method for 2-D electrical impedance tomography are studied. The method is based on Nachman's uniqueness proof [Ann. of Math. 143 (1996)] that applies to twice differentiable conductivities. However, the reconstruction algorithm has been successfully applied to(More)