Electrical Impedance Tomography (EIT) is a non-invasive imaging technique that reconstructs the internal conductivity distribution of a medium by solving an inverse problem based on surface electrical measurements. This thesis explores inversion algorithms for EIT with a particular focus on Tikhonov regularization, SVD filtering, and iterative solvers such as LSQR. Simulations are conducted in both 2D and 3D domains, with an emphasis on managing ill-posedness and measurement noise. The practical implications are shown through test cases involving environmental monitoring of subsurface contamination. The work provides a complete framework that connects theoretical modeling, numerical solution, and algorithmic stability for real-world EIT applications.
La Tomografia di Impedenza Elettrica (EIT) è una tecnica di imaging non invasiva che consente di ricostruire la distribuzione interna della conducibilità di un mezzo a partire da misure elettriche effettuate sulla sua superficie. Questa tesi approfondisce gli algoritmi di inversione per l’EIT, concentrandosi in particolare sulla regolarizzazione di Tikhonov, sul filtraggio tramite SVD e sui metodi iterativi come LSQR. Le simulazioni sono sviluppate sia in domini 2D che 3D, affrontando le problematiche legate alla mal-posedness e al rumore di misura. L’applicazione pratica è dimostrata mediante casi di studio sul monitoraggio ambientale di contaminazioni sotterranee. Il lavoro offre un quadro completo che unisce modellazione teorica, soluzione numerica e stabilità algoritmica in ambito EIT.
Electrical impedance tomography for non-invasive underground diagnosis
BAKHTIYOROV, SHERZODBEK
2024/2025
Abstract
Electrical Impedance Tomography (EIT) is a non-invasive imaging technique that reconstructs the internal conductivity distribution of a medium by solving an inverse problem based on surface electrical measurements. This thesis explores inversion algorithms for EIT with a particular focus on Tikhonov regularization, SVD filtering, and iterative solvers such as LSQR. Simulations are conducted in both 2D and 3D domains, with an emphasis on managing ill-posedness and measurement noise. The practical implications are shown through test cases involving environmental monitoring of subsurface contamination. The work provides a complete framework that connects theoretical modeling, numerical solution, and algorithmic stability for real-world EIT applications.File | Dimensione | Formato | |
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2025_07_Bakhtiyorov.pdf
solo utenti autorizzati a partire dal 01/07/2026
Descrizione: Reconstruction of the current density field obtained using generalized least squares (Tikhonov regularization)
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1.91 MB
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1.91 MB | Adobe PDF | Visualizza/Apri |
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https://hdl.handle.net/10589/239624