Direct Reconstructions of Conductivities from Boundary Measurements

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 Isaacson [Inverse Problems 16 (2000), pp.681-699] presented a new numerical reconstruction method that solves the nonlinear problem directly without iteration. The method was verified with non-noisy rotationally symmetric examples. In this paper the method is extended by introducing a new regularization scheme, which is analyzed theoretically and tested on symmetric and non-symmetric numerical examples containing computer simulated noise.