A learning-based method for solving ill-posed nonlinear inverse problems: A simulation study of lung EIT

Jin Keun Seo, Kang Cheol Kim, Ariungerel Jargal, Kyounghun Lee, Bastian Harrach

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

This paper proposes a new approach for solving ill-posed nonlinear inverse problems. For ease of explanation of the proposed approach, we use the example of lung electrical impedance tomography (EIT), which is known to be a nonlinear and ill-posed inverse problem. Conventionally, penaltybased regularization methods have been used to deal with the ill-posed problem. However, experiences over the last three decades have shown methodological limitations in utilizing prior knowledge about tracking expected imaging features for medical diagnosis. The proposed method’s paradigm is completely different from conventional approaches; the proposed reconstruction uses a variety of training data sets to generate a low dimensional manifold of approximate solutions, which allows conversion of the ill-posed problem to a well-posed one. Variational autoencoder was used to produce a compact and dense representation for lung EIT images with a low dimensional latent space. Then, we learn a robust connection between the EIT data and the low dimensional latent data. Numerical simulations validate the effectiveness and feasibility of the proposed approach.

Original languageEnglish
Pages (from-to)1275-1295
Number of pages21
JournalSIAM Journal on Imaging Sciences
Volume12
Issue number3
DOIs
Publication statusPublished - 2019 Jan 1

Fingerprint

Nonlinear Inverse Problems
Electrical Impedance Tomography
Acoustic impedance
Ill-posed Problem
Lung
Inverse problems
Tomography
Simulation Study
Regularization Method
Prior Knowledge
Inverse Problem
Approximate Solution
Paradigm
Imaging
Imaging techniques
Numerical Simulation
Computer simulation
Learning

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

Seo, Jin Keun ; Kim, Kang Cheol ; Jargal, Ariungerel ; Lee, Kyounghun ; Harrach, Bastian. / A learning-based method for solving ill-posed nonlinear inverse problems : A simulation study of lung EIT. In: SIAM Journal on Imaging Sciences. 2019 ; Vol. 12, No. 3. pp. 1275-1295.
@article{7dac299cdcca4c44a37ca9aeadbc3967,
title = "A learning-based method for solving ill-posed nonlinear inverse problems: A simulation study of lung EIT",
abstract = "This paper proposes a new approach for solving ill-posed nonlinear inverse problems. For ease of explanation of the proposed approach, we use the example of lung electrical impedance tomography (EIT), which is known to be a nonlinear and ill-posed inverse problem. Conventionally, penaltybased regularization methods have been used to deal with the ill-posed problem. However, experiences over the last three decades have shown methodological limitations in utilizing prior knowledge about tracking expected imaging features for medical diagnosis. The proposed method’s paradigm is completely different from conventional approaches; the proposed reconstruction uses a variety of training data sets to generate a low dimensional manifold of approximate solutions, which allows conversion of the ill-posed problem to a well-posed one. Variational autoencoder was used to produce a compact and dense representation for lung EIT images with a low dimensional latent space. Then, we learn a robust connection between the EIT data and the low dimensional latent data. Numerical simulations validate the effectiveness and feasibility of the proposed approach.",
author = "Seo, {Jin Keun} and Kim, {Kang Cheol} and Ariungerel Jargal and Kyounghun Lee and Bastian Harrach",
year = "2019",
month = "1",
day = "1",
doi = "10.1137/18M1222600",
language = "English",
volume = "12",
pages = "1275--1295",
journal = "SIAM Journal on Imaging Sciences",
issn = "1936-4954",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "3",

}

A learning-based method for solving ill-posed nonlinear inverse problems : A simulation study of lung EIT. / Seo, Jin Keun; Kim, Kang Cheol; Jargal, Ariungerel; Lee, Kyounghun; Harrach, Bastian.

In: SIAM Journal on Imaging Sciences, Vol. 12, No. 3, 01.01.2019, p. 1275-1295.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A learning-based method for solving ill-posed nonlinear inverse problems

T2 - A simulation study of lung EIT

AU - Seo, Jin Keun

AU - Kim, Kang Cheol

AU - Jargal, Ariungerel

AU - Lee, Kyounghun

AU - Harrach, Bastian

PY - 2019/1/1

Y1 - 2019/1/1

N2 - This paper proposes a new approach for solving ill-posed nonlinear inverse problems. For ease of explanation of the proposed approach, we use the example of lung electrical impedance tomography (EIT), which is known to be a nonlinear and ill-posed inverse problem. Conventionally, penaltybased regularization methods have been used to deal with the ill-posed problem. However, experiences over the last three decades have shown methodological limitations in utilizing prior knowledge about tracking expected imaging features for medical diagnosis. The proposed method’s paradigm is completely different from conventional approaches; the proposed reconstruction uses a variety of training data sets to generate a low dimensional manifold of approximate solutions, which allows conversion of the ill-posed problem to a well-posed one. Variational autoencoder was used to produce a compact and dense representation for lung EIT images with a low dimensional latent space. Then, we learn a robust connection between the EIT data and the low dimensional latent data. Numerical simulations validate the effectiveness and feasibility of the proposed approach.

AB - This paper proposes a new approach for solving ill-posed nonlinear inverse problems. For ease of explanation of the proposed approach, we use the example of lung electrical impedance tomography (EIT), which is known to be a nonlinear and ill-posed inverse problem. Conventionally, penaltybased regularization methods have been used to deal with the ill-posed problem. However, experiences over the last three decades have shown methodological limitations in utilizing prior knowledge about tracking expected imaging features for medical diagnosis. The proposed method’s paradigm is completely different from conventional approaches; the proposed reconstruction uses a variety of training data sets to generate a low dimensional manifold of approximate solutions, which allows conversion of the ill-posed problem to a well-posed one. Variational autoencoder was used to produce a compact and dense representation for lung EIT images with a low dimensional latent space. Then, we learn a robust connection between the EIT data and the low dimensional latent data. Numerical simulations validate the effectiveness and feasibility of the proposed approach.

UR - http://www.scopus.com/inward/record.url?scp=85073791464&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85073791464&partnerID=8YFLogxK

U2 - 10.1137/18M1222600

DO - 10.1137/18M1222600

M3 - Article

AN - SCOPUS:85073791464

VL - 12

SP - 1275

EP - 1295

JO - SIAM Journal on Imaging Sciences

JF - SIAM Journal on Imaging Sciences

SN - 1936-4954

IS - 3

ER -