Fast methods for shape reconstruction in Electrical Resistance Tomography

Abstract Electrical Resistance Tomography (ERT) is a body of methods and techniques aimed to reconstruct the spatial distribution of the conductivity of a material starting from the knowledge of boundary measurements such as, for instance, the Neumann-to-Dirichlet map. This inverse problem is ill-posed and nonlinear and, therefore, its solution require a considerable computational effort. In this paper we present a comparison between three fast non-iterative reconstruction methods for locating inclusions in an otherwise homogeneous material (for both 2D and 3D geometries). These methods, potentially, are candidate for real-time applications.

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

[2]  Michael Vogelius,et al.  A direct impedance tomography algorithm for locating small inhomogeneities , 2003, Numerische Mathematik.

[3]  A. Kirsch,et al.  A simple method for solving inverse scattering problems in the resonance region , 1996 .

[4]  Denys Breysse,et al.  ELECTRICAL RESISTIVITY MEASUREMENT APPLIED TO CRACKING ASSESSMENT ON REINFORCED CONCRETE STRUCTURES IN CIVIL ENGINEERING , 2003 .

[5]  Antonello Tamburrino,et al.  Non-iterative imaging method for experimental data inversion in eddy current tomography , 2012 .

[6]  Andreas Kirsch,et al.  Characterization of the shape of a scattering obstacle using the spectral data of the far field operator , 1998 .

[7]  V. Isakov.  Uniqueness and stability in multi-dimensional inverse problems , 1993 .

[8]  Antonello Tamburrino.  Monotonicity based imaging methods for elliptic and parabolic inverse problems , 2006 .

[9]  Martin Hanke,et al.  Recent progress in electrical impedance tomography , 2003 .

[10]  H. Lev-Ari,et al.  The time-reversal technique re-interpreted: subspace-based signal processing for multi-static target location , 2000, Proceedings of the 2000 IEEE Sensor Array and Multichannel Signal Processing Workshop. SAM 2000 (Cat. No.00EX410).

[11]  Feng Dong,et al.  Electrical resistance tomography for locating inclusions using analytical boundary element integrals and their partial derivatives , 2010 .

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

[13]  Giovanni Santarato,et al.  Non-invasive characterisation of ancient foundations in Venice using the electrical resistivity imaging technique , 2006 .

[14]  Margaret Cheney,et al.  The Linear Sampling Method and the MUSIC Algorithm , 2001 .

[15]  Eric T. Chung,et al.  Electrical impedance tomography using level set representation and total variational regularization , 2005 .

[16]  A. Nachman,et al.  Reconstructions from boundary measurements , 1988 .

[17]  Ramani Duraiswami,et al.  Efficient 2D and 3D electrical impedance tomography using dual reciprocity boundary element techniques , 1998 .

[18]  Robert V. Kohn,et al.  Determining conductivity by boundary measurements , 1984 .

[19]  Antonello Tamburrino,et al.  A new non-iterative inversion method for electrical resistance tomography , 2002 .

[20]  Antonello Tamburrino,et al.  Fast methods for quantitative eddy-current tomography of conductive materials , 2006, IEEE Transactions on Magnetics.

[21]  Avner Friedman,et al.  Identification of small inhomogeneities of extreme conductivity by boundary measurements: a theorem on continuous dependence , 1989 .

[22]  Antonello Tamburrino,et al.  Experimental validation of a fast non-iterative imaging algorithm for eddy current tomography , 2010 .

[23]  A. Kirsch.  The MUSIC-algorithm and the factorization method in inverse scattering theory for inhomogeneous media , 2002 .

[24]  Daniel Rittel,et al.  Experimental crack identification using electrical impedance tomography , 2002 .

[25]  Takashi Ohe,et al.  A numerical method for finding the convex hull of polygonal cavities using the enclosure method , 2002 .

[26]  Boris Rubinsky,et al.  Front-tracking image reconstruction algorithm for EIT-monitored cryosurgery using the boundary element method , 2005, Physiological measurement.

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

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

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

[30]  V. Isakov.  Appendix -- Function Spaces , 2017 .

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