Comparing D-bar and common regularization-based methods for electrical impedance tomography

Objective: To compare D-bar difference reconstruction with regularized linear reconstruction in electrical impedance tomography. Approach: A standard regularized linear approach using a Laplacian penalty and the GREIT method for comparison to the D-bar difference images. Simulated data was generated using a circular phantom with small objects, as well as a ‘Pac-Man’ shaped conductivity target. An L-curve method was used for parameter selection in both D-bar and the regularized methods. Main results: We found that the D-bar method had a more position independent point spread function, was less sensitive to errors in electrode position and behaved differently with respect to additive noise than the regularized methods. Significance: The results allow a novel pathway between traditional and D-bar algorithm comparison.

[1]  J. C. Newell,et al.  Impedance images of the chest , 1992, 1992 14th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

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

[3]  Martin Burger,et al.  Inverse problems in imaging , 2013 .

[4]  William R B Lionheart.  Uniqueness, Shape, and Dimension in EIT , 1999 .

[5]  J C Newell,et al.  Imaging cardiac activity by the D-bar method for electrical impedance tomography , 2006, Physiological measurement.

[6]  Dianne P. O'Leary,et al.  The Use of the L-Curve in the Regularization of Discrete Ill-Posed Problems , 1993, SIAM J. Sci. Comput..

[7]  Andy Adler,et al.  3D EIT image reconstruction with GREIT , 2016, Physiological measurement.

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

[9]  Andy Adler,et al.  FEM electrode refinement for electrical impedance tomography , 2013, 2013 35th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC).

[10]  Otmar Scherzer,et al.  Handbook of Mathematical Methods in Imaging , 2015, Handbook of Mathematical Methods in Imaging.

[11]  François Treves.  Pseudodifferential Operators and Applications , 1985 .

[12]  N. J. Avis,et al.  Image reconstruction in Electrical Impedance Tomography using filtered back-projection , 1992, 1992 14th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[13]  Andy Adler,et al.  Shape Deformation in Two-Dimensional Electrical Impedance Tomography , 2012, IEEE Transactions on Medical Imaging.

[14]  Samuli Siltanen,et al.  Numerical solution method for the dbar-equation in the plane , 2004 .

[15]  M. K. Pidcock,et al.  Some Mathematical Aspects of Electrical Impedance Tomography , 1988 .

[16]  Thomas J. Yorkey,et al.  Comparing reconstruction methods for electrical impedance tomography , 1987, Annals of Biomedical Engineering.

[17]  S J Hamilton,et al.  Robust computation in 2D absolute EIT (a-EIT) using D-bar methods with the ‘exp’ approximation , 2017, Physiological measurement.

[18]  Matti Lassas,et al.  REGULARIZED D-BAR METHOD FOR THE INVERSE CONDUCTIVITY PROBLEM , 2009 .

[19]  Samuli Siltanen,et al.  Linear and Nonlinear Inverse Problems with Practical Applications , 2012, Computational science and engineering.

[20]  G. Vainikko.  Fast Solvers of the Lippmann-Schwinger Equation , 2000 .

[21]  David Isaacson,et al.  Reconstructions of chest phantoms by the D-bar method for electrical impedance tomography , 2004, IEEE Transactions on Medical Imaging.

[22]  William R B Lionheart,et al.  GREIT: a unified approach to 2D linear EIT reconstruction of lung images , 2009, Physiological measurement.

[23]  Andy Adler,et al.  Whither lung EIT: Where are we, where do we want to go and what do we need to get there? , 2012, Physiological measurement.