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Electrical Impedance Tomography (EIT) has emerged as a valuable medical imaging modality, which visualizes the conductivity distribution of a subject by performing multi-electrode impedance measurements. EIT finds applications in monitoring lung and cardiac function, brain imaging and the detection of malignant tissues. Its mobility, outstanding temporal resolution and the absence of ionizing radiation make it particularly suitable for repetitive real-time monitoring and diagnostics, especially in radiation-sensitive populations, such as neonates. This paper presents a methodological review of EIT image reconstruction approaches spanning from traditional linear regularization and back-projection to more recent techniques, including deep learning, sparse Bayesian learning and non-linear shape-driven reconstruction. Linear and non-linear reconstruction approaches are distinguished, as well as time, frequency difference and absolute reconstruction ones. The exposition includes a concise elaboration of the methodologies&#x2019; mathematical foundations and algorithmic deployment, with particular attention to recent advancements. For each approach, an assessment of its merits and drawbacks is given, providing implementation considerations, imaging performance and relevant applications.

Advances in Electrical Impedance Tomography Inverse Problem Solution Methods: From Traditional Regularization to Deep Learning