A Forward-Backward Strategy for Handling Non-linearity in Electrical Impedance Tomography

• Published in: Computational Science and Its Applications - ICCSA 2021 Vol. 12951; pp. 635 - 651
• Main Authors: Huska, Martin, Lazzaro, Damiana, Morigi, Serena
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2021; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: EIT inverse problem; Forward-backward algorithm; Nonlinear optimization; Regularization
• ISBN: 9783030869694; 3030869695
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-030-86970-0_44

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.