This book is a unified presentation of new methods, algorithms, and select applications that are the foundations of multidimensional image reconstruction by discrete tomographic methods. The self-contained chapters, written by leading mathematicians, engineers, and computer scientists, present cutting-edge research and results in the field. Following an introduction that reports the recent literature of the field, the book explores various mathematical and computational problems of discrete tomography including new applications to electron microscopy, materials science, nondestructive testing, and diagnostic medicine.

Professionals, researchers, practitioners, and students in mathematics, computer imaging, biomedical imaging, computer science, and image processing will find the book to be a useful guide and reference to state-of-the-art research, methods, and applications.

Klappentext

Advances in Discrete Tomography and Its Applications is a unified presentation of new methods, algorithms, and select applications that are the foundations of multidimensional image reconstruction by discrete tomographic methods. The self-contained chapters, written by leading mathematicians, engineers, and computer scientists, present cutting-edge research and results in the field.

Three main areas are covered: foundations, algorithms, and practical applications. Following an introduction that reports the recent literature of the field, the book explores various mathematical and computational problems of discrete tomography including new applications.

Topics and Features:

• introduction to discrete point X-rays

• uniqueness and additivity in discrete tomography

• network flow algorithms for discrete tomography

• convex programming and variational methods

• applications to electron microscopy, materials science, nondestructive testing, and diagnostic medicine

Professionals, researchers, practitioners, and students in mathematics, computer imaging, biomedical imaging, computer science, and image processing will find the book to be a useful guide and reference to state-of-the-art research, methods, and applications.

Inhalt
Foundations of Discrete Tomography.- An Introduction to Discrete Point X-Rays.- Reconstruction of Q-Convex Lattice Sets.- Algebraic Discrete Tomography.- Uniqueness and Additivity for n-Dimensional Binary Matrices with Respect to Their 1-Marginals.- Constructing (0,1)-Matrices with Given Line Sums and Certain Fixed Zeros.- Reconstruction of Binary Matrices under Adjacency Constraints.- Discrete Tomography Reconstruction Algorithms.- Decomposition Algorithms for Reconstructing Discrete Sets with Disjoint Components.- Network Flow Algorithms for Discrete Tomography.- A Convex Programming Algorithm for Noisy Discrete Tomography.- Variational Reconstruction with DC-Programming.- Applications of Discrete Tomography.- Direct Image Reconstruction-Segmentation, as Motivated by Electron Microscopy.- Discrete Tomography for Generating Grain Maps of Polycrystals.- Discrete Tomography Methods for Nondestructive Testing.- Emission Discrete Tomography.- Application of a Discrete Tomography Approach to Computerized Tomography.