Towards time-independent electrical impedance tomography reconstruction

Motivation, Goal and Task - Motivation: Electrical Impedance Tomography (EIT) is a non-invasive imaging technique with significant potential in medical diagnostics (e.g., lung monitoring, cancer detection) and industrial applications. However, its clinical adoption remains limited due to three critical challenges inherent to time-independent reconstruction: (1) the ill-posed inverse problem amplifies small measurement errors into severe artifacts, (2) hardware imperfections and modeling inaccuracies degrade robustness, and (3) existing algorithms like Gauss-Newton and D-Bar suffer from computational inefficiency, instability in real-world conditions, or lack of generalizability. Traditional neural network approaches often require calibration data or fail to handle diverse conductivity distributions. This work addresses these gaps by advancing reconstruction quality, computational efficiency, and noise resilience for absolute and frequency-differential EIT. Goal: The dissertation pursues two complementary approaches to improve time-independent EIT: Artificial Neural Network (ANN): Design a rotation-invariant architecture to directly map boundary voltages to conductivity distributions, prioritizing noise robustness and generalizability across diverse scenarios. D-Bar Algorithm: Refine this direct method for absolute and frequency-differential reconstructions while addressing practical limitations like contact impedance, non-circular domains, and limited spatial resolution through radar data fusion. Task: The work develops two approaches: a rotation-invariant ANN trained on FEM simulations and tank data for direct voltage-to-conductivity mapping, and an enhanced D-Bar algorithm for practically available measurement devices. Validation focuses on synthetic FEM datasets and experimental tank measurements with conductive targets. Major Scientific Contributions - ANN: The proposed ANN architecture establishes new capabilities in absolute EIT reconstruction through three fundamental innovations. First, the network's rotation-invariant design inherently handles arbitrary domain orientations through weight sharing and electrode position encoding, eliminating the need for explicit coordinate transformations. Second, training exclusively on synthetic datasets generated through Finite Element Method simulations demonstrates generalizability to real-world laboratory and animal data. Third, the architecture constitutes the first successful application of neural networks to time-independent absolute EIT reconstruction, validated through systematic experiments on tank phantoms with conductive targets and porcine trial datasets showing physiologically plausible conductivity discrimination between major organs. D-Bar: This work advances practical implementation of the D-Bar method through two key contributions. The first develops a complete operational pipeline within the open-source EIDORS framework. This implementation demonstrates robust experimental performance through comprehensive tank phantom verification with multiple conductive targets. The second introduces a novel pre-processing methodology enabling absolute reconstructions from pure four-electrode measurements – a critical advancement for real world applications. The modified algorithm maintains compatibility with frequency-differential and absolute EIT operation while addressing historical limitations in handling contact impedance variations. Together, these developments bridge the gap between theoretical D-Bar formulations and practically deployable EIT systems.