Impedance imaging and Markov chain Monte Carlo methods

E Somersalo; J Kaipio; M Vauhkonen; D Baroudi; S Jarvenpaa

Impedance imaging and Markov chain Monte Carlo methods

E Somersalo^*, J Kaipio, M Vauhkonen, D Baroudi, S Jarvenpaa

^*Corresponding author for this work

Department of Mathematics and Systems Analysis

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

9 Citations (Scopus)

Abstract

The article discusses the electrical impedance imaging problem (EIT) from a Bayesian point of view. We discuss two essentially different EIT problems: The first one is the static problem of estimating the resistivity distribution of a body from the static current/voltage measurements on the surface of the body. The other problem is a gas temperature distribution retrieval problem by resistivity measurements of metal filaments placed in the gas funnel. In these examples, the prior information contains inequality constraints and non-smooth functionals. Consequently, gradient-based maximum likelihood search algorithms converge poorly. To overcome this difficulty, we study the possibility of using a Markov chain Monte Carlo algorithm to explore the posterior distribution.

Original language	English
Title of host publication	COMPUTATIONAL, EXPERIMENTAL, AND NUMERICAL METHODS FOR SOLVING ILL-POSED INVERSE IMAGING PROBLEMS: MEDICAL AND NONMEDICAL APPLICATIONS
Editors	RL Barbour, MJ Carvlin, MA Fiddy
Publisher	SPIE
Pages	175-185
Number of pages	11
ISBN (Print)	0-8194-2593-1
Publication status	Published - 1997
MoE publication type	A4 Conference publication
Event	Conference on Computational, Experimental, and Numerical Methods for Solving Ill-Posed Inverse Imaging Problems: Medical and Nonmedical Applications - San Diego, United States Duration: 30 Jul 1997 → 31 Jul 1997

Publication series

Name	PROCEEDINGS OF THE SOCIETY OF PHOTO-OPTICAL INSTRUMENTATION ENGINEERS (SPIE)
Publisher	SPIE-INT SOC OPTICAL ENGINEERING
Volume	3171
ISSN (Print)	0277-786X

Conference

Conference	Conference on Computational, Experimental, and Numerical Methods for Solving Ill-Posed Inverse Imaging Problems: Medical and Nonmedical Applications
Country/Territory	United States
City	San Diego
Period	30/07/1997 → 31/07/1997

Keywords

electrical impedance tomography
Bayesian methods
inverse problems
MCMC
temperature tomography

Cite this

Somersalo, E., Kaipio, J., Vauhkonen, M., Baroudi, D., & Jarvenpaa, S. (1997). Impedance imaging and Markov chain Monte Carlo methods. In RL. Barbour, MJ. Carvlin, & MA. Fiddy (Eds.), COMPUTATIONAL, EXPERIMENTAL, AND NUMERICAL METHODS FOR SOLVING ILL-POSED INVERSE IMAGING PROBLEMS: MEDICAL AND NONMEDICAL APPLICATIONS (pp. 175-185). (PROCEEDINGS OF THE SOCIETY OF PHOTO-OPTICAL INSTRUMENTATION ENGINEERS (SPIE); Vol. 3171). SPIE.

Somersalo, E ; Kaipio, J ; Vauhkonen, M et al. / Impedance imaging and Markov chain Monte Carlo methods. COMPUTATIONAL, EXPERIMENTAL, AND NUMERICAL METHODS FOR SOLVING ILL-POSED INVERSE IMAGING PROBLEMS: MEDICAL AND NONMEDICAL APPLICATIONS. editor / RL Barbour ; MJ Carvlin ; MA Fiddy. SPIE, 1997. pp. 175-185 (PROCEEDINGS OF THE SOCIETY OF PHOTO-OPTICAL INSTRUMENTATION ENGINEERS (SPIE)).

@inproceedings{ad467d42e0d548d397fe65620c6ef0ab,

title = "Impedance imaging and Markov chain Monte Carlo methods",

abstract = "The article discusses the electrical impedance imaging problem (EIT) from a Bayesian point of view. We discuss two essentially different EIT problems: The first one is the static problem of estimating the resistivity distribution of a body from the static current/voltage measurements on the surface of the body. The other problem is a gas temperature distribution retrieval problem by resistivity measurements of metal filaments placed in the gas funnel. In these examples, the prior information contains inequality constraints and non-smooth functionals. Consequently, gradient-based maximum likelihood search algorithms converge poorly. To overcome this difficulty, we study the possibility of using a Markov chain Monte Carlo algorithm to explore the posterior distribution.",

keywords = "electrical impedance tomography, Bayesian methods, inverse problems, MCMC, temperature tomography",

author = "E Somersalo and J Kaipio and M Vauhkonen and D Baroudi and S Jarvenpaa",

year = "1997",

language = "English",

isbn = "0-8194-2593-1",

series = "PROCEEDINGS OF THE SOCIETY OF PHOTO-OPTICAL INSTRUMENTATION ENGINEERS (SPIE)",

publisher = "SPIE",

pages = "175--185",

editor = "RL Barbour and MJ Carvlin and MA Fiddy",

booktitle = "COMPUTATIONAL, EXPERIMENTAL, AND NUMERICAL METHODS FOR SOLVING ILL-POSED INVERSE IMAGING PROBLEMS: MEDICAL AND NONMEDICAL APPLICATIONS",

address = "United States",

note = "Conference on Computational, Experimental, and Numerical Methods for Solving Ill-Posed Inverse Imaging Problems: Medical and Nonmedical Applications ; Conference date: 30-07-1997 Through 31-07-1997",

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Somersalo, E, Kaipio, J, Vauhkonen, M, Baroudi, D & Jarvenpaa, S 1997, Impedance imaging and Markov chain Monte Carlo methods. in RL Barbour, MJ Carvlin & MA Fiddy (eds), COMPUTATIONAL, EXPERIMENTAL, AND NUMERICAL METHODS FOR SOLVING ILL-POSED INVERSE IMAGING PROBLEMS: MEDICAL AND NONMEDICAL APPLICATIONS. PROCEEDINGS OF THE SOCIETY OF PHOTO-OPTICAL INSTRUMENTATION ENGINEERS (SPIE), vol. 3171, SPIE, pp. 175-185, Conference on Computational, Experimental, and Numerical Methods for Solving Ill-Posed Inverse Imaging Problems: Medical and Nonmedical Applications, San Diego, California, United States, 30/07/1997.

Impedance imaging and Markov chain Monte Carlo methods. / Somersalo, E; Kaipio, J; Vauhkonen, M et al.
COMPUTATIONAL, EXPERIMENTAL, AND NUMERICAL METHODS FOR SOLVING ILL-POSED INVERSE IMAGING PROBLEMS: MEDICAL AND NONMEDICAL APPLICATIONS. ed. / RL Barbour; MJ Carvlin; MA Fiddy. SPIE, 1997. p. 175-185 (PROCEEDINGS OF THE SOCIETY OF PHOTO-OPTICAL INSTRUMENTATION ENGINEERS (SPIE); Vol. 3171).

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

TY - GEN

T1 - Impedance imaging and Markov chain Monte Carlo methods

AU - Somersalo, E

AU - Kaipio, J

AU - Vauhkonen, M

AU - Baroudi, D

AU - Jarvenpaa, S

PY - 1997

Y1 - 1997

N2 - The article discusses the electrical impedance imaging problem (EIT) from a Bayesian point of view. We discuss two essentially different EIT problems: The first one is the static problem of estimating the resistivity distribution of a body from the static current/voltage measurements on the surface of the body. The other problem is a gas temperature distribution retrieval problem by resistivity measurements of metal filaments placed in the gas funnel. In these examples, the prior information contains inequality constraints and non-smooth functionals. Consequently, gradient-based maximum likelihood search algorithms converge poorly. To overcome this difficulty, we study the possibility of using a Markov chain Monte Carlo algorithm to explore the posterior distribution.

AB - The article discusses the electrical impedance imaging problem (EIT) from a Bayesian point of view. We discuss two essentially different EIT problems: The first one is the static problem of estimating the resistivity distribution of a body from the static current/voltage measurements on the surface of the body. The other problem is a gas temperature distribution retrieval problem by resistivity measurements of metal filaments placed in the gas funnel. In these examples, the prior information contains inequality constraints and non-smooth functionals. Consequently, gradient-based maximum likelihood search algorithms converge poorly. To overcome this difficulty, we study the possibility of using a Markov chain Monte Carlo algorithm to explore the posterior distribution.

KW - electrical impedance tomography

KW - Bayesian methods

KW - inverse problems

KW - MCMC

KW - temperature tomography

M3 - Conference article in proceedings

SN - 0-8194-2593-1

T3 - PROCEEDINGS OF THE SOCIETY OF PHOTO-OPTICAL INSTRUMENTATION ENGINEERS (SPIE)

SP - 175

EP - 185

BT - COMPUTATIONAL, EXPERIMENTAL, AND NUMERICAL METHODS FOR SOLVING ILL-POSED INVERSE IMAGING PROBLEMS: MEDICAL AND NONMEDICAL APPLICATIONS

A2 - Barbour, RL

A2 - Carvlin, MJ

A2 - Fiddy, MA

PB - SPIE

T2 - Conference on Computational, Experimental, and Numerical Methods for Solving Ill-Posed Inverse Imaging Problems: Medical and Nonmedical Applications

Y2 - 30 July 1997 through 31 July 1997

ER -

Somersalo E, Kaipio J, Vauhkonen M, Baroudi D, Jarvenpaa S. Impedance imaging and Markov chain Monte Carlo methods. In Barbour RL, Carvlin MJ, Fiddy MA, editors, COMPUTATIONAL, EXPERIMENTAL, AND NUMERICAL METHODS FOR SOLVING ILL-POSED INVERSE IMAGING PROBLEMS: MEDICAL AND NONMEDICAL APPLICATIONS. SPIE. 1997. p. 175-185. (PROCEEDINGS OF THE SOCIETY OF PHOTO-OPTICAL INSTRUMENTATION ENGINEERS (SPIE)).

Impedance imaging and Markov chain Monte Carlo methods

Abstract

Publication series

Conference

Keywords

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Cite this