### Abstract

A well-established reconstruction algorithm for electrical impedance tomography uses a finite-element method to model the forwards problem using Neumann boundary conditions. The reconstruction is then obtained by solving the inverse problem through an iterative non-linear least-squares fit of the model electrode voltages to the measured voltages. It is also usual to apply Tikhonov regularization to improve the condition of the inverse problem. However, such regularization introduces artefacts into the solution estimate. We present a quasi-single-step reconstruction technique based on a weakly regularized solution constructed from the final Jacobian of the standard iterative scheme, with filtering to act as a 'mollifier'. This reconstruction has well-defined spectral properties, since it approximates a filtered version of the original impedance distribution. Some illustrative results are given for 2D resistance tomography.

Original language | English |
---|---|

Number of pages | 6 |

Journal | Measurement Science and Technology |

Volume | 10 |

Publication status | Published - 1999 |

### Keywords

- electrical impedance tomography
- approximate inverse
- Zernike polynomials
- Tikhonov regularization
- mollifier
- RESISTANCE TOMOGRAPHY

### Cite this

*Measurement Science and Technology*,

*10*.

**An electrical impedance tomography algorithm with well-defined spectral properties.** / Player, M A ; van Weereld, J ; Hutchison, J M S ; Allen, A R ; Shang, L .

Research output: Contribution to journal › Article

*Measurement Science and Technology*, vol. 10.

}

TY - JOUR

T1 - An electrical impedance tomography algorithm with well-defined spectral properties

AU - Player, M A

AU - van Weereld, J

AU - Hutchison, J M S

AU - Allen, A R

AU - Shang, L

PY - 1999

Y1 - 1999

N2 - A well-established reconstruction algorithm for electrical impedance tomography uses a finite-element method to model the forwards problem using Neumann boundary conditions. The reconstruction is then obtained by solving the inverse problem through an iterative non-linear least-squares fit of the model electrode voltages to the measured voltages. It is also usual to apply Tikhonov regularization to improve the condition of the inverse problem. However, such regularization introduces artefacts into the solution estimate. We present a quasi-single-step reconstruction technique based on a weakly regularized solution constructed from the final Jacobian of the standard iterative scheme, with filtering to act as a 'mollifier'. This reconstruction has well-defined spectral properties, since it approximates a filtered version of the original impedance distribution. Some illustrative results are given for 2D resistance tomography.

AB - A well-established reconstruction algorithm for electrical impedance tomography uses a finite-element method to model the forwards problem using Neumann boundary conditions. The reconstruction is then obtained by solving the inverse problem through an iterative non-linear least-squares fit of the model electrode voltages to the measured voltages. It is also usual to apply Tikhonov regularization to improve the condition of the inverse problem. However, such regularization introduces artefacts into the solution estimate. We present a quasi-single-step reconstruction technique based on a weakly regularized solution constructed from the final Jacobian of the standard iterative scheme, with filtering to act as a 'mollifier'. This reconstruction has well-defined spectral properties, since it approximates a filtered version of the original impedance distribution. Some illustrative results are given for 2D resistance tomography.

KW - electrical impedance tomography

KW - approximate inverse

KW - Zernike polynomials

KW - Tikhonov regularization

KW - mollifier

KW - RESISTANCE TOMOGRAPHY

M3 - Article

VL - 10

JO - Measurement Science and Technology

JF - Measurement Science and Technology

SN - 0957-0233

ER -