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Electrical Impedance Tomography (EIT) is a powerful imaging technique withdiverse applications, e.g., medical diagnosis, industrial monitoring, andenvironmental studies. The EIT inverse problem is about inferring the internalconductivity distribution of an object from measurements taken on its boundary.It is severely ill-posed, necessitating advanced computational methods foraccurate image reconstructions. Recent years have witnessed significantprogress, driven by innovations in analytic-based approaches and deep learning.This review explores techniques for solving the EIT inverse problem, focusingon the interplay between contemporary deep learning-based strategies andclassical analytic-based methods. Four state-of-the-art deep learningalgorithms are rigorously examined, harnessing the representationalcapabilities of deep neural networks to reconstruct intricate conductivitydistributions. In parallel, two analytic-based methods, rooted in mathematicalformulations and regularisation techniques, are dissected for their strengthsand limitations. These methodologies are evaluated through various numericalexperiments, encompassing diverse scenarios that reflect real-worldcomplexities. A suite of performance metrics is employed to assess the efficacyof these methods. These metrics collectively provide a nuanced understanding ofthe methods' ability to capture essential features and delineate complexconductivity patterns. One novel feature of the study is the incorporation ofvariable conductivity scenarios, introducing a level of heterogeneity thatmimics textured inclusions. This departure from uniform conductivityassumptions mimics realistic scenarios where tissues or materials exhibitspatially varying electrical properties. Exploring how each method responds tosuch variable conductivity scenarios opens avenues for understanding theirrobustness and adaptability.

Electrical Impedance Tomography: A Fair Comparative Study on Deep Learning and Analytic-based Approaches