Electrical Impedance Tomography (EIT) is known to be a nonlinear and ill-posed inverse problem. Conventional penalty-based regularization methods rely on the linearized model of the nonlinear forward operator. However, the linearized problem is only a rough approximation of the real situation, where the measurements can further contain unavoidable noise. The proposed reconstruction variational framework allows to turn the complete nonlinear ill-posed EIT problem into a sequence of regularized linear least squares optimization problems via a forward-backward splitting strategy, thus converting the ill-posed problem to a well-posed one. The framework can easily integrate suitable penalties to enforce smooth or piecewise-constant conductivity reconstructions depending on prior information. Numerical experiments validate the effectiveness and feasibility of the proposed approach.

A forward-backward strategy for handling non-linearity in Electrical Impedence Tomography / morigi serena; lazzaro damiana; huska martin. - STAMPA. - 12951:(2021), pp. 635-651. [10.1007/978-3-030-86970-0_44]

A forward-backward strategy for handling non-linearity in Electrical Impedence Tomography

morigi serena
;
lazzaro damiana;huska martin
2021

Abstract

Electrical Impedance Tomography (EIT) is known to be a nonlinear and ill-posed inverse problem. Conventional penalty-based regularization methods rely on the linearized model of the nonlinear forward operator. However, the linearized problem is only a rough approximation of the real situation, where the measurements can further contain unavoidable noise. The proposed reconstruction variational framework allows to turn the complete nonlinear ill-posed EIT problem into a sequence of regularized linear least squares optimization problems via a forward-backward splitting strategy, thus converting the ill-posed problem to a well-posed one. The framework can easily integrate suitable penalties to enforce smooth or piecewise-constant conductivity reconstructions depending on prior information. Numerical experiments validate the effectiveness and feasibility of the proposed approach.
2021
Computational Science and Its Applications – ICCSA 2021. PT III
635
651
A forward-backward strategy for handling non-linearity in Electrical Impedence Tomography / morigi serena; lazzaro damiana; huska martin. - STAMPA. - 12951:(2021), pp. 635-651. [10.1007/978-3-030-86970-0_44]
morigi serena; lazzaro damiana; huska martin
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/832117
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