Algorithms in Tomography and Related Inverse Problems—A Review

Abstract

In the ever-evolving landscape of tomographic imaging algorithms, this literature review explores a diverse array of themes shaping the field’s progress. It encompasses foundational principles, special innovative approaches, tomographic implementation algorithms, and applications of tomography in medicine, natural sciences, remote sensing, and seismology. This choice is to show off the diversity of tomographic applications and simultaneously the new trends in tomography in recent years. Accordingly, the evaluation of backprojection methods for breast tomographic reconstruction is highlighted. After that, multi-slice fusion takes center stage, promising real-time insights into dynamic processes and advanced diagnosis. Computational efficiency, especially in methods for accelerating tomographic reconstruction algorithms on commodity PC graphics hardware, is also presented. In geophysics, a deep learning-based approach to ground-penetrating radar (GPR) data inversion propels us into the future of geological and environmental sciences. We venture into Earth sciences with global seismic tomography: the inverse problem and beyond, understanding the Earth’s subsurface through advanced inverse problem solutions and pushing boundaries. Lastly, optical coherence tomography is reviewed in basic applications for revealing tiny biological tissue structures. This review presents the main categories of applications of tomography, providing a deep insight into the methods and algorithms that have been developed so far so that the reader who wants to deal with the subject is fully informed.