American Institute of Mathematical Sciences

Advanced
February  2008, 2(1): 43-61. doi: 10.3934/ipi.2008.2.43

2D EIT reconstructions using Calderon's method

Jutta Bikowski 1, and  Jennifer L. Mueller 2,

1. 

Department of Mathematics, Colorado State University, Fort Collins, CO 80523, United States
2. 

Department of Mathematics, Colorado State University, Fort Collins, CO 80523,, United States

Received  June 2007 Revised  January 2008 Published  January 2008

The pioneering work ''On an inverse boundary value problem'' by A. Calderón has inspired a multitude of research, both theoretical and numerical, on the inverse conductivity problem (ICP). The problem has an important application in a medical imaging technique known as electrical impedance tomography (EIT) in which currents are applied on electrodes on the surface of a body, the resulting voltages are measured, and the ICP is solved to determine the conductivity distribution in the interior of the body, which is then displayed to form an image. In this article, the reconstruction method proposed by Calderón is implemented in 2D for both simulated and experimental data including perfusion data collected on a human chest.
Keywords: electrical impedance tomography, Calderón's method., inverse conductivity problem.
Mathematics Subject Classification: Primary: 35R30, 35R05; Secondary: 65N2.
Citation: Jutta Bikowski, Jennifer L. Mueller. 2D EIT reconstructions using Calderon's method. Inverse Problems & Imaging, 2008, 2 (1) : 43-61. doi: 10.3934/ipi.2008.2.43
[1]

Albert Clop, Daniel Faraco, Alberto Ruiz. Stability of Calderón's inverse conductivity problem in the plane for discontinuous conductivities. Inverse Problems & Imaging, 2010, 4 (1) : 49-91. doi: 10.3934/ipi.2010.4.49
[2]

Ville Kolehmainen, Matti Lassas, Petri Ola, Samuli Siltanen. Recovering boundary shape and conductivity in electrical impedance tomography. Inverse Problems & Imaging, 2013, 7 (1) : 217-242. doi: 10.3934/ipi.2013.7.217
[3]

Dong liu, Ville Kolehmainen, Samuli Siltanen, Anne-maria Laukkanen, Aku Seppänen. Estimation of conductivity changes in a region of interest with electrical impedance tomography. Inverse Problems & Imaging, 2015, 9 (1) : 211-229. doi: 10.3934/ipi.2015.9.211
[4]

Gen Nakamura, Päivi Ronkanen, Samuli Siltanen, Kazumi Tanuma. Recovering conductivity at the boundary in three-dimensional electrical impedance tomography. Inverse Problems & Imaging, 2011, 5 (2) : 485-510. doi: 10.3934/ipi.2011.5.485
[5]

Matteo Santacesaria. Note on Calderón's inverse problem for measurable conductivities. Inverse Problems & Imaging, 2019, 13 (1) : 149-157. doi: 10.3934/ipi.2019008
[6]

Ke Zhang, Maokun Li, Fan Yang, Shenheng Xu, Aria Abubakar. Electrical impedance tomography with multiplicative regularization. Inverse Problems & Imaging, 2019, 13 (6) : 1139-1159. doi: 10.3934/ipi.2019051
[7]

Bastian Gebauer. Localized potentials in electrical impedance tomography. Inverse Problems & Imaging, 2008, 2 (2) : 251-269. doi: 10.3934/ipi.2008.2.251
[8]

Fabrice Delbary, Rainer Kress. Electrical impedance tomography using a point electrode inverse scheme for complete electrode data. Inverse Problems & Imaging, 2011, 5 (2) : 355-369. doi: 10.3934/ipi.2011.5.355
[9]

Hiroshi Isozaki. Inverse boundary value problems in the horosphere - A link between hyperbolic geometry and electrical impedance tomography. Inverse Problems & Imaging, 2007, 1 (1) : 107-134. doi: 10.3934/ipi.2007.1.107
[10]

Kari Astala, Jennifer L. Mueller, Lassi Päivärinta, Allan Perämäki, Samuli Siltanen. Direct electrical impedance tomography for nonsmooth conductivities. Inverse Problems & Imaging, 2011, 5 (3) : 531-549. doi: 10.3934/ipi.2011.5.531
[11]

Helmut Harbrecht, Thorsten Hohage. A Newton method for reconstructing non star-shaped domains in electrical impedance tomography. Inverse Problems & Imaging, 2009, 3 (2) : 353-371. doi: 10.3934/ipi.2009.3.353
[12]

Nuutti Hyvönen, Harri Hakula, Sampsa Pursiainen. Numerical implementation of the factorization method within the complete electrode model of electrical impedance tomography. Inverse Problems & Imaging, 2007, 1 (2) : 299-317. doi: 10.3934/ipi.2007.1.299
[13]

Sarah Jane Hamilton, Andreas Hauptmann, Samuli Siltanen. A data-driven edge-preserving D-bar method for electrical impedance tomography. Inverse Problems & Imaging, 2014, 8 (4) : 1053-1072. doi: 10.3934/ipi.2014.8.1053
[14]

Melody Alsaker, Sarah Jane Hamilton, Andreas Hauptmann. A direct D-bar method for partial boundary data electrical impedance tomography with a priori information. Inverse Problems & Imaging, 2017, 11 (3) : 427-454. doi: 10.3934/ipi.2017020
[15]

Oleg Yu. Imanuvilov, Masahiro Yamamoto. Calderón problem for Maxwell's equations in cylindrical domain. Inverse Problems & Imaging, 2014, 8 (4) : 1117-1137. doi: 10.3934/ipi.2014.8.1117
[16]

Petteri Piiroinen, Martin Simon. Probabilistic interpretation of the Calderón problem. Inverse Problems & Imaging, 2017, 11 (3) : 553-575. doi: 10.3934/ipi.2017026
[17]

Kim Knudsen, Matti Lassas, Jennifer L. Mueller, Samuli Siltanen. Regularized D-bar method for the inverse conductivity problem. Inverse Problems & Imaging, 2009, 3 (4) : 599-624. doi: 10.3934/ipi.2009.3.599
[18]

Liliana Borcea, Fernando Guevara Vasquez, Alexander V. Mamonov. Study of noise effects in electrical impedance tomography with resistor networks. Inverse Problems & Imaging, 2013, 7 (2) : 417-443. doi: 10.3934/ipi.2013.7.417
[19]

Nicolay M. Tanushev, Luminita Vese. A piecewise-constant binary model for electrical impedance tomography. Inverse Problems & Imaging, 2007, 1 (2) : 423-435. doi: 10.3934/ipi.2007.1.423
[20]

Nuutti Hyvönen, Lassi Päivärinta, Janne P. Tamminen. Enhancing D-bar reconstructions for electrical impedance tomography with conformal maps. Inverse Problems & Imaging, 2018, 12 (2) : 373-400. doi: 10.3934/ipi.2018017

2019 Impact Factor: 1.373

Tools

Metrics

  • PDF downloads (92)
  • HTML views (0)
  • Cited by (27)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences