Computed Tomography: Algorithms, Insight, and Just Enough Theory (Fundamentals of Algorithms)

Edited by Per Christian Hansen, Jakob Sauer Jørgensen, and William R. B. Lionheart With contributions from Martin S. Andersen, K. Joost Batenburg, Yiqiu Dong, Eric Todd Quinto, and Jan Sijbers This book describes fundamental computational methods for image reconstruction in computed tomography (CT) with a focus on a pedagogical presentation of these methods and their underlying concepts. Insights into the advantages, limitations, and theoretical and computational aspects of the methods are included, giving a balanced presentation that allows readers to understand and implement CT reconstruction algorithms. Unique in its emphasis on the interplay between modeling, computing, and algorithm development, Computed Tomography: Algorithms, Insight, and Just Enough Theory develops the mathematical and computational aspects of three main classes of reconstruction methods: classical filtered back-projection, algebraic iterative methods, and variational methods based on nonlinear numerical optimization algorithms. It spotlights the link between CT and numerical methods, which is rarely discussed in current literature, and describes the effects of incomplete data using both microlocal analysis and singular value decomposition (SVD). This book sets the stage for further exploration of CT algorithms. Readers will be able to grasp the underlying mathematical models to motivate and derive the basic principles of CT reconstruction and will gain basic understanding of fundamental computational challenges of CT, such as the influence of noisy and incomplete data, as well as the reconstruction capabilities and the convergence of the iterative algorithms. Exercises using MATLAB are included, allowing readers to experiment with the algorithms and making the book suitable for teaching and self-study. Computed Tomography: Algorithms, Insight, and Just Enough Theory is primarily aimed at students, researchers, and practitioners interested in the computational aspects of X-ray CT and is also relevant for anyone working with other forms of tomography, such as neutron and electron tomography, that share the same mathematical formulation. With its basis in lecture notes developed for a PhD course, it is appropriate as a textbook for courses on computational methods for X-ray CT and computational methods for inverse problems.

Per Christian Hansen is a professor of scientific computing at the Technical University of Denmark. He is a SIAM Fellow and a Villum Investigator. He currently heads a research initiative on computational uncertainty quantification for inverse problems. Jakob Sauer Jørgensen is a senior researcher at the Technical University of Denmark and a Presidential Fellow from The University of Manchester. His current work focuses on algorithms and software for CT and uncertainty quantification. William R. B. Lionheart is a professor of applied mathematics at The University of Manchester. He works on analytical, numerical, and practical aspects of a wide range of imaging and inverse problems. His current work includes X-ray, electron, and neutron tomography as well as increasingly rich tomography methods involving spectral, diffraction, or polarimetric data to produce nonscalar 3D images.