Convex Source Support and Its Application to Electric Impedance Tomography

The aim in electric impedance tomography is to recover the conductivity inside a physical body from boundary measurements of current and voltage. In many situations of practical importance, the investigated object has known background conductivity but is contaminated by inhomogeneities. In this work, we try to extract all possible information about the support of such inclusions inside a two-dimensional object from only one pair of measurements of impedance tomography. Our noniterative and computationally cheap method is based on the concept of the convex source support, which stems from earlier works of Kusiak, Sylvester, and the authors. The functionality of our algorithm is demonstrated by various numerical experiments.

[1]  Henry C. Thacher,et al.  Applied and Computational Complex Analysis. , 1988 .

[2]  John Sylvester,et al.  A scattering support for broadband sparse far field measurements , 2005 .

[3]  S. B. Childs,et al.  INVERSE PROBLEMS IN PARTIAL DIFFERENTIAL EQUATIONS. , 1968 .

[4]  Martin Hanke,et al.  On real-time algorithms for the location search of discontinuous conductivities with one measurement , 2008 .

[5]  M. Hanke,et al.  Source supports in electrostatics , 2008 .

[6]  Steven Kusiak,et al.  The scattering support , 2003 .

[7]  J. Seo,et al.  Numerical identification of discontinuous conductivity coefficients , 1997 .

[8]  M. Hanke,et al.  Numerical implementation of two noniterative methods for locating inclusions by impedance tomography , 2000 .

[9]  David Isaacson,et al.  Electrical Impedance Tomography , 1999, SIAM Rev..

[10]  K. Kunisch,et al.  Level-set function approach to an inverse interface problem , 2001 .

[11]  William Rundell,et al.  The determination of a discontinuity in a conductivity from a single boundary measurement , 1998 .

[12]  Harri Hakula,et al.  The Factorization Method Applied to the Complete Electrode Model of Impedance Tomography , 2008, SIAM J. Appl. Math..

[13]  Kari Astala,et al.  Calderon's inverse conductivity problem in the plane , 2006 .

[14]  Harri Hakula,et al.  Two noniterative algorithms for locating inclusions using one electrode measurement of electric impedance tomography , 2008 .

[15]  J. Sylvester,et al.  A global uniqueness theorem for an inverse boundary value problem , 1987 .

[16]  Liliana Borcea,et al.  Addendum to 'Electrical impedance tomography' , 2003 .

[17]  R. Kress,et al.  Nonlinear integral equations and the iterative solution for an inverse boundary value problem , 2005 .

[18]  A. Nachman,et al.  Global uniqueness for a two-dimensional inverse boundary value problem , 1996 .

[19]  Nuutti Hyvönen,et al.  Approximating idealized boundary data of electric impedance tomography by electrode measurements , 2009 .

[20]  A. Siamj.,et al.  COMPLETE ELECTRODE MODEL OF ELECTRICAL IMPEDANCE TOMOGRAPHY : APPROXIMATION PROPERTIES AND CHARACTERIZATION OF INCLUSIONS , 2004 .

[21]  Roland Potthast,et al.  A 'range test' for determining scatterers with unknown physical properties , 2003 .

[22]  Ohin Kwon,et al.  A real time algorithm for the location search of discontinuous conductivities with one measurement , 2002 .

[23]  Steven Kusiak,et al.  The Convex Scattering Support in a Background Medium , 2005, SIAM J. Math. Anal..

[24]  J. Sylvester.  Notions of support for far fields , 2006 .

[25]  C. DeWitt-Morette,et al.  Mathematical Analysis and Numerical Methods for Science and Technology , 1990 .

[26]  Kurt Bryan,et al.  Numerical recovery of certain discontinuous electrical conductivities , 1991 .

[27]  Houssem Haddar,et al.  The Convex Back-Scattering Support , 2005, SIAM J. Appl. Math..