Computed tomography : algorithms, insight, and just enough theory / edited by Per Christian Hansen, Jakob Sauer Jørgensen, William R.B. Lionheart ; with contributions from Martin S. Andersen, K. Joost Batenburg, Yiqiu Dong, Eric Todd Quinto, and Jan Sijbers.

Format:

Book

Contributor:

Hansen, Per Christian, editor.

Jørgensen, Jakob Sauer, editor.

Lionheart, William, editor.

Society for Industrial and Applied Mathematics, publisher.

Series:

Fundamentals of algorithms ; FA18.

Fundamentals of algorithms ; 18

Language:

English

Subjects (All):

Geometric tomography.

Tomography--Data processing.

Tomography.

Physical Description:

1 online resource (xvii, 337 pages) : illustrations.

Place of Publication:

Philadelphia, Pennsylvania : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104) : Mathematical Optimization Society, [2021]

System Details:

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

Summary:

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; 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.

Contents:

Introduction / P.C. Hansen, J.S. Jørgensen, W.R.B. Lionheart

Just enough analysis : functions, operators, and inverse problems / W.R.B. Lionheart

Just enough linear algebra / P.C. Hansen

Just enough physics / J. Sijbers, J.S. Jørgensen

The radon transform / J.S. Jørgensen, W.R.B. Lionheart

Filtered back-projection / J.S. Jørgensen, W.R.B. Lionheart

Singular values and functions of the radon transform / P.C. Hansen, W.R.B. Lionheart

Limited-data tomography / E.T. Quinto

Discretization models and the system matrix / K.J. Batenburg, P.C. Hansen, J.S. Jørgensen

SVD analysis of tomography problems / P.C. Hansen

Algebraic iterative reconstruction methods / P.C. Hansen

Regularization techniques for tomography problems / Y. Dong

Optimization methods for tomography / M.S. Andersen

Looking ahead / P.C. Hansen, J.S. Jørgensen, W.R.B. Lionheart.

Notes:

Includes bibliographical references (pages 319-331) and index.

Description based on title page of print version.

ISBN:

1-61197-667-7

Publisher Number:

FA18 SIAM