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 journalArticlepeer-review

18 Citations (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

Bibliographical note

Funding Information:
\ast Received by the editors October 24, 2018; accepted for publication (in revised form) April 23, 2019; published electronically July 2, 2019. https://doi.org/10.1137/18M1222600 Funding: The work of the first and second authors was supported by the National Research Foundation of Korea (NRF) grants 2015R1A5A1009350 and 2017R1A2B20005661. The work of the third and fourth authors was supported by the National Research Foundation of Korea (NRF) grant 2017R1E1A1A03070653. \dagger Department of Computational Science and Engineering, Yonsei University, Seoul, 120-749, Korea (seoj@ yonsei.ac.kr, kangcheol@yonsei.ac.kr, j.ariungerel@gmail.com, imlkh84@gmail.com). \ddagger Department of Mathematics, Goethe University Frankfurt, 60325 Frankfurt am Main, Germany (harrach@ math.uni-frankfurt.de).

Publisher Copyright:
© 2019 Society for Industrial and Applied Mathematics.

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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