  Electrical Impedance Tomography (EIT) is a powerful imaging technique with
diverse applications, e.g., medical diagnosis, industrial monitoring, and
environmental studies. The EIT inverse problem is about inferring the internal
conductivity distribution of an object from measurements taken on its boundary.
It is severely ill-posed, necessitating advanced computational methods for
accurate image reconstructions. Recent years have witnessed significant
progress, driven by innovations in analytic-based approaches and deep learning.
This review explores techniques for solving the EIT inverse problem, focusing
on the interplay between contemporary deep learning-based strategies and
classical analytic-based methods. Four state-of-the-art deep learning
algorithms are rigorously examined, harnessing the representational
capabilities of deep neural networks to reconstruct intricate conductivity
distributions. In parallel, two analytic-based methods, rooted in mathematical
formulations and regularisation techniques, are dissected for their strengths
and limitations. These methodologies are evaluated through various numerical
experiments, encompassing diverse scenarios that reflect real-world
complexities. A suite of performance metrics is employed to assess the efficacy
of these methods. These metrics collectively provide a nuanced understanding of
the methods' ability to capture essential features and delineate complex
conductivity patterns. One novel feature of the study is the incorporation of
variable conductivity scenarios, introducing a level of heterogeneity that
mimics textured inclusions. This departure from uniform conductivity
assumptions mimics realistic scenarios where tissues or materials exhibit
spatially varying electrical properties. Exploring how each method responds to
such variable conductivity scenarios opens avenues for understanding their
robustness and adaptability.
