# American Institute of Mathematical Sciences

May  2007, 1(2): 423-435. doi: 10.3934/ipi.2007.1.423

## A piecewise-constant binary model for electrical impedance tomography

 1 Department of Mathematics, University of California, Los Angeles, 405 Hilgard Avenue,Los Angeles, CA 90095-1555, United States

Received  January 2007 Published  April 2007

In this paper, we consider the electrical impedance tomography problem in a computational approach. This inverse problem is the recovery of the electrical conductivity $\sigma$ in a domain from boundary measurements, given in the form of the Neumann-to-Dirichlet map. We formulate the inverse problem as a variational one, with a fitting term and a regularization term. We restrict the minimization with respect to the unknown $\sigma$ to piecewise-constant functions defined on rectangular domains in two dimensions. We borrow image segmentation techniques to solve the minimization problem. Several experimental results of conductivity reconstruction from synthetic data are shown, with and without noise, that validate the proposed method.
Citation: Nicolay M. Tanushev, Luminita Vese. A piecewise-constant binary model for electrical impedance tomography. Inverse Problems and Imaging, 2007, 1 (2) : 423-435. doi: 10.3934/ipi.2007.1.423
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