View in EDS

A Learning-Based Method for Solving Ill-Posed Nonlinear Inverse Problems: A Simulation Study of Lung EIT.

Saved in:
Bibliographic Details
Title: A Learning-Based Method for Solving Ill-Posed Nonlinear Inverse Problems: A Simulation Study of Lung EIT.
Authors: Jin Keun Seo1 seoj@yonsei.ac.kr, Kang Cheol Kim1 kangcheol@yonsei.ac.kr, Ariungerel Jargal1 j.ariungerel@gmail.com, Kyounghun Lee1 imlkh84@gmail.com, Harrach, Bastian2 harrach@math.uni-frankfurt.de
Source: SIAM Journal on Imaging Sciences. 2019, Vol. 12 Issue 3, p1275-1295. 21p.
Subjects: Inverse problems, Nonlinear equations, Electrical impedance tomography, Lungs, Diagnostic imaging
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. [ABSTRACT FROM AUTHOR]
Copyright of SIAM Journal on Imaging Sciences is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
Description
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. [ABSTRACT FROM AUTHOR]
ISSN:19364954
DOI:10.1137/18M1222600