2019
DOI: 10.1137/18m1222600
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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, penalty-based 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 imagin… Show more

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Cited by 92 publications
(50 citation statements)
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“…[30,21], and monotonicity arguments were also used to prove stability results, cf. [28,24,62,12]. The recent follow-up paper [26] extends the results to general potentials q ∈ L ∞ (Ω) in the fractional diffusion case and proves Lipschitz stability with finitely many measurements.…”
Section: Discussionmentioning
confidence: 88%
“…[30,21], and monotonicity arguments were also used to prove stability results, cf. [28,24,62,12]. The recent follow-up paper [26] extends the results to general potentials q ∈ L ∞ (Ω) in the fractional diffusion case and proves Lipschitz stability with finitely many measurements.…”
Section: Discussionmentioning
confidence: 88%
“…On the methodological side, this work builds upon [48,53] and stems from the theory of combining monotonicity estimates with localized potentials, cf. [9,13,25,35,43,45,46,[50][51][52][56][57][58][59]61,94] for related works, and [29,[37][38][39][40]49,54,55,60,85,97,99,100,102,106] for practical monotonicity-based reconstruction methods. In this work, the monotonicity and convexity of the forward function is based on the so-called monotonicity relation which goes back to Ikehata, Kang, Seo, and Sheen [65,70].…”
Section: Introductionmentioning
confidence: 99%
“…The former type enhances the resolution of relatively lowresolution images generated by conventional methods [27,34]. The latter type directly learns mappings from measured data to images [35,36]. In this study, we developed a method of the second type by adopting a multilayer perceptron (MLP), which is one of the deep-learning techniques.…”
Section: Introductionmentioning
confidence: 99%