Two abstract formulations to Electrical Impedance Tomography

• Ano de defesa: 2023
• Autor(a) principal: Avalos, Josué Daniel Díaz
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Abordagem all-at-once; All-at-once approach; Complete electrode model; Continuum model; Dualidade; Duality; Electrical impedance tomography; Modelo contínuo; Modelo de electrodo completo; Tomografia por impedância elétrica
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/45/45132/tde-02032023-175531/

Electrical Impedance Tomography (EIT) is an imaging modality that seeks to recover the conductivity distribution inside a physical body from electrical measurements taken on the body surface. In this thesis, two contributions to EIT are presented. The first is a theoretical framework that unifies the formulation and analysis of EIT models. There, the weak formulations of the EIT models and the current-voltage maps are generalized, and dual properties that reveal the link between the formulations in terms of electric potentials and current fields are found. The second is the regularization of an all-at-once formulation of the EIT inverse problem. Three regularized problems are formulated based on the classic Tikhonov, Ivanov, and Morozov regularizations, and the existence, stability, and convergence of regularized solutions are proved. In both developments, several EIT models are admitted and numerical examples to illustrate our theoretical results are provided.