Detecting stochastic inclusions in electrical impedance tomography

This work considers the inclusion detection problem of electrical impedance tomography with stochastic conductivities. It is shown that a conductivity anomaly with a random conductivity can be identified by applying the Factorization Method or the Monotonicity Method to the mean value of the corresponding Neumann-to-Dirichlet map provided that the anomaly has high enough contrast in the sense of expectation. The theoretical results are complemented by numerical examples in two spatial dimensions.

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

[2]  Imaging and time reversal in random media , 2001 .

[3]  Gunther Uhlmann,et al.  Electrical impedance tomography and Calderón's problem , 2009 .

[4]  Henrik Garde,et al.  Convergence and regularization for monotonicity-based shape reconstruction in electrical impedance tomography , 2015, Numerische Mathematik.

[5]  Harri Hakula,et al.  On computation of test dipoles for factorization method , 2009 .

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

[7]  Nuutti Hyvönen,et al.  Factorization method and irregular inclusions in electrical impedance tomography , 2007 .

[8]  Bastian von Harrach,et al.  Recent Progress on the Factorization Method for Electrical Impedance Tomography , 2013, Comput. Math. Methods Medicine.

[9]  Andreas Kirsch,et al.  A factorization scheme for determining conductivity contrasts in impedance tomography , 2011 .

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

[11]  Samuli Siltanen,et al.  Probing for electrical inclusions with complex spherical waves , 2007 .

[12]  Martin Brühl,et al.  Explicit Characterization of Inclusions in Electrical Impedance Tomography , 2001, SIAM J. Math. Anal..

[13]  Jin Keun Seo,et al.  Detecting Inclusions in Electrical Impedance Tomography Without Reference Measurements , 2009, SIAM J. Appl. Math..

[14]  Andreas Kirsch,et al.  The factorization method for a class of inverse elliptic problems , 2005 .

[15]  D. C. Barber,et al.  Three-dimensional electrical impedance tomography , 1996, Nature.

[16]  Lauri Mustonen.  Numerical study of a parametric parabolic equation and a related inverse boundary value problem , 2015, 1506.01559.

[17]  David S. Holder,et al.  Electrical Impedance Tomography : Methods, History and Applications , 2004 .

[18]  M. Lassas,et al.  Inverse acoustic scattering problem in half-space with anisotropic random impedance , 2014, 1407.2481.

[19]  Eung Je Woo,et al.  Factorization Method and Its Physical Justification in Frequency-Difference Electrical Impedance Tomography , 2010, IEEE Transactions on Medical Imaging.

[20]  Jin Keun Seo,et al.  Exact Shape-Reconstruction by One-Step Linearization in Electrical Impedance Tomography , 2010, SIAM J. Math. Anal..

[21]  Liliana Borcea,et al.  Electrical impedance tomography , 2002 .

[22]  William R B Lionheart.  EIT reconstruction algorithms: pitfalls, challenges and recent developments. , 2004, Physiological measurement.

[23]  Armin Lechleiter,et al.  A regularization technique for the factorization method , 2006 .

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

[25]  E. Saksman,et al.  Inverse Scattering Problem for a Two Dimensional Random Potential , 2008 .

[26]  E. Somersalo,et al.  Existence and uniqueness for electrode models for electric current computed tomography , 1992 .

[27]  Lauri Mustonen.  Parametric differential equations and inverse diffusivity problem , 2014 .

[28]  M. Soleimani,et al.  Conditional Bayes reconstruction for ERT data using resistance monotonicity information , 2006 .

[29]  Claude Jeffrey Gittelson,et al.  Sparse tensor discretizations of high-dimensional parametric and stochastic PDEs* , 2011, Acta Numerica.

[30]  Masaru Ikehata,et al.  Size estimation of inclusion , 1998 .

[31]  D. Isaacson,et al.  Electrode models for electric current computed tomography , 1989, IEEE Transactions on Biomedical Engineering.

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

[33]  Bastian von Harrach,et al.  Monotonicity-Based Shape Reconstruction in Electrical Impedance Tomography , 2013, SIAM J. Math. Anal..

[34]  Bastian Gebauer,et al.  Localized potentials in electrical impedance tomography , 2008 .

[35]  Guillaume Bal,et al.  Time-reversal-based detection in random media , 2005 .

[36]  S. Schmitt,et al.  The factorization method for EIT in the case of mixed inclusions , 2009 .

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

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

[39]  Jin Keun Seo,et al.  The inverse conductivity problem with one measurement: stability and estimation of size , 1997 .

[40]  Harri Hakula,et al.  Numerical implementation of the factorization method within the complete electrode model of electrical impedance tomography , 2007 .

[41]  N I Grinberg,et al.  The Factorization Method for Inverse Problems , 2007 .

[42]  J. Hayashi.  [Sampling methods]. , 1982, Josanpu zasshi = The Japanese journal for midwife.

[43]  Andy Adler,et al.  Electrical Impedance Tomography , 2019, Wiley Encyclopedia of Electrical and Electronics Engineering.

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

[45]  Marko Vauhkonen,et al.  Suitability of a PXI platform for an electrical impedance tomography system , 2008 .

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

[47]  Bastian von Harrach,et al.  Resolution Guarantees in Electrical Impedance Tomography , 2015, IEEE Transactions on Medical Imaging.

[48]  Simon Arridge,et al.  The factorization method for three dimensional electrical impedance tomography , 2013, 1312.1479.

[49]  Lassi Päivärinta,et al.  On imaging obstacles inside inhomogeneous media , 2007 .

[50]  Birgit Schappel,et al.  The Factorization Method for Electrical Impedance Tomography in the Half-Space , 2008, SIAM J. Appl. Math..

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

[52]  Guillaume Bal,et al.  Time Reversal and Refocusing in Random Media , 2003, SIAM J. Appl. Math..

[53]  Jin Keun Seo,et al.  Regularizing a linearized EIT reconstruction method using a sensitivity-based factorization method , 2014, 1811.07616.

[54]  Bastian Gebauer,et al.  The Factorization Method for Real Elliptic Problems , 2006 .

[55]  R H Bayford,et al.  Bioimpedance tomography (electrical impedance tomography). , 2006, Annual review of biomedical engineering.