T-scan electrical impedance imaging system for anomaly detection

Habib Ammari, Ohin Kwon, Jin Keun Seo, Eung J.E. Woo

Research output: Contribution to journalArticle

35 Citations (Scopus)

Abstract

We consider an inverse conductivity problem arising in anomaly detections with its mathematical model based on the T-Scan system (breast cancer detection system). In this model, we try to detect an anomaly D from one or two sets of measured data that are available only on a small portion Γ of the boundary of the subject Ω. In practice, Ω differs in each subject, so our detection algorithm should not depend much on the global geometry of Ω. The purpose of this work is to provide a mathematical ground for the reconstruction of a rough feature of D which is stable against any measurement noise and any change of geometry ∂Ω. Based on rigorous estimates with a simplified model, we found an approximation that gives a noniterative detection algorithm of finding a useful feature of anomaly. We also present a multifrequency approach to handling the case where the complex conductivity of the background is not homogeneous and is not known a priori.

Original languageEnglish
Pages (from-to)252-266
Number of pages15
JournalSIAM Journal on Applied Mathematics
Volume65
Issue number1
DOIs
Publication statusPublished - 2005 Apr 15

Fingerprint

Acoustic impedance
Anomaly Detection
Imaging System
Imaging systems
Impedance
Anomaly
Geometry
Inverse Conductivity Problem
Mathematical models
Breast Cancer
Conductivity
Rough
Mathematical Model
Model-based
Approximation
Model
Estimate

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

Cite this

Ammari, Habib ; Kwon, Ohin ; Seo, Jin Keun ; Woo, Eung J.E. / T-scan electrical impedance imaging system for anomaly detection. In: SIAM Journal on Applied Mathematics. 2005 ; Vol. 65, No. 1. pp. 252-266.
@article{34d091b7758e40a7a102ed467db689a8,
title = "T-scan electrical impedance imaging system for anomaly detection",
abstract = "We consider an inverse conductivity problem arising in anomaly detections with its mathematical model based on the T-Scan system (breast cancer detection system). In this model, we try to detect an anomaly D from one or two sets of measured data that are available only on a small portion Γ of the boundary of the subject Ω. In practice, Ω differs in each subject, so our detection algorithm should not depend much on the global geometry of Ω. The purpose of this work is to provide a mathematical ground for the reconstruction of a rough feature of D which is stable against any measurement noise and any change of geometry ∂Ω. Based on rigorous estimates with a simplified model, we found an approximation that gives a noniterative detection algorithm of finding a useful feature of anomaly. We also present a multifrequency approach to handling the case where the complex conductivity of the background is not homogeneous and is not known a priori.",
author = "Habib Ammari and Ohin Kwon and Seo, {Jin Keun} and Woo, {Eung J.E.}",
year = "2005",
month = "4",
day = "15",
doi = "10.1137/S003613990343375X",
language = "English",
volume = "65",
pages = "252--266",
journal = "SIAM Journal on Applied Mathematics",
issn = "0036-1399",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "1",

}

T-scan electrical impedance imaging system for anomaly detection. / Ammari, Habib; Kwon, Ohin; Seo, Jin Keun; Woo, Eung J.E.

In: SIAM Journal on Applied Mathematics, Vol. 65, No. 1, 15.04.2005, p. 252-266.

Research output: Contribution to journalArticle

TY - JOUR

T1 - T-scan electrical impedance imaging system for anomaly detection

AU - Ammari, Habib

AU - Kwon, Ohin

AU - Seo, Jin Keun

AU - Woo, Eung J.E.

PY - 2005/4/15

Y1 - 2005/4/15

N2 - We consider an inverse conductivity problem arising in anomaly detections with its mathematical model based on the T-Scan system (breast cancer detection system). In this model, we try to detect an anomaly D from one or two sets of measured data that are available only on a small portion Γ of the boundary of the subject Ω. In practice, Ω differs in each subject, so our detection algorithm should not depend much on the global geometry of Ω. The purpose of this work is to provide a mathematical ground for the reconstruction of a rough feature of D which is stable against any measurement noise and any change of geometry ∂Ω. Based on rigorous estimates with a simplified model, we found an approximation that gives a noniterative detection algorithm of finding a useful feature of anomaly. We also present a multifrequency approach to handling the case where the complex conductivity of the background is not homogeneous and is not known a priori.

AB - We consider an inverse conductivity problem arising in anomaly detections with its mathematical model based on the T-Scan system (breast cancer detection system). In this model, we try to detect an anomaly D from one or two sets of measured data that are available only on a small portion Γ of the boundary of the subject Ω. In practice, Ω differs in each subject, so our detection algorithm should not depend much on the global geometry of Ω. The purpose of this work is to provide a mathematical ground for the reconstruction of a rough feature of D which is stable against any measurement noise and any change of geometry ∂Ω. Based on rigorous estimates with a simplified model, we found an approximation that gives a noniterative detection algorithm of finding a useful feature of anomaly. We also present a multifrequency approach to handling the case where the complex conductivity of the background is not homogeneous and is not known a priori.

UR - http://www.scopus.com/inward/record.url?scp=16244384993&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=16244384993&partnerID=8YFLogxK

U2 - 10.1137/S003613990343375X

DO - 10.1137/S003613990343375X

M3 - Article

VL - 65

SP - 252

EP - 266

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 1

ER -