BookDOI
Advances in discrete tomography and its applications
Gabor T. Herman,Attila Kuba +1 more
TLDR
A. Kuba and G.T. Herman Discrete point X-ray (DPT) reconstruction as discussed by the authors is a well-known technique in the field of discrete tomography.Abstract:
ANHA Series Preface Preface List of Contributors Introduction / A. Kuba and G.T. Herman Part I. Foundations of Discrete Tomography An Introduction to Discrete Point X-Rays / P. Dulio, R.J. Gardner, and C. Peri Reconstruction of Q-Convex Lattice Sets / S. Brunetti and A. Daurat Algebraic Discrete Tomography / L. Hajdu and R. Tijdeman Uniqueness and Additivity for n-Dimensional Binary Matrices with Respect to Their 1-Marginals / E. Vallejo Constructing (0, 1)-Matrices with Given Line Sums and Certain Fixed Zeros / R.A. Brualdi and G. Dahl Reconstruction of Binary Matrices under Adjacency Constraints / S. Brunetti, M.C. Costa, A. Frosini, F. Jarray, and C. Picouleau Part II. Discrete Tomography Reconstruction Algorithms Decomposition Algorithms for Reconstructing Discrete Sets with Disjoint Components / P. Balazs Network Flow Algorithms for Discrete Tomography / K.J. Batenburg A Convex Programming Algorithm for Noisy Discrete Tomography / T.D. Capricelli and P.L. Combettes Variational Reconstruction with DC-Programming / C. Schnoerr, T. Schule, and S. Weber Part III. Applications of Discrete Tomography Direct Image Reconstruction-Segmentation, as Motivated by Electron Microscopy / Hstau Y. Liao and Gabor T. Herman Discrete Tomography for Generating Grain Maps of Polycrystals / A. Alpers, L. Rodek, H.F. Poulsen, E. Knudsen, G.T. Herman Discrete Tomography Methods for Nondestructive Testing / J. Baumann, Z. Kiss, S. Krimmel, A. Kuba, A. Nagy, L. Rodek, B. Schillinger, and J. Stephan Emission Discrete Tomography / E. Barcucci, A. Frosini, A. Kuba, A. Nagy, S. Rinaldi, M. Samal, and S. Zopf Application of a Discrete Tomography Approach to Computerized Tomography / Y. Gerard and F. Feschet Indexread more
Citations
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Journal ArticleDOI
Quantitative X-ray tomography
Eric Maire,Philip J. Withers +1 more
TL;DR: In this paper, the authors review the current state of the art as CT transforms from a qualitative diagnostic tool to a quantitative one, including the use of iterative reconstruction strategies suited to specific segmentation tasks and emerging methods that provide more insight than conventional attenuation based tomography.
Reference BookDOI
Handbook of mathematical methods in imaging
TL;DR: In this article, the Mumford and Shah Model and its applications in total variation image restoration are discussed. But the authors focus on the reconstruction of 3D information, rather than the analysis of the image.
Journal ArticleDOI
DART: A Practical Reconstruction Algorithm for Discrete Tomography
Kees Joost Batenburg,Jan Sijbers +1 more
TL;DR: An iterative reconstruction algorithm for discrete tomography, called discrete algebraic reconstruction technique (DART), which is capable of computing more accurate reconstructions from a small number of projection images, or from asmall angular range, than alternative methods.
Journal ArticleDOI
3D imaging of nanomaterials by discrete tomography.
Kees Joost Batenburg,Sara Bals,Jan Sijbers,Christian Kübel,Paul A. Midgley,J. C. Hernandez,Ute Kaiser,Ezequiel Roberto Encina,Eduardo A. Coronado,G. Van Tendeloo +9 more
TL;DR: The basic principles of DART are described and it is shown that it can be applied successfully to three different types of samples, consisting of embedded ErSi(2) nanocrystals, a carbon nanotube grown from a catalyst particle and a single gold nanoparticle, respectively.
Journal ArticleDOI
Image reconstruction from a small number of projections
Gabor T. Herman,Ran Davidi +1 more
TL;DR: It is demonstrated that sometimes an algorithm based on total variation minimization produces medically-desirable reconstructions in computerized tomography (CT) even from a small number of projections, and that such a reconstruction is not guaranteed to provide the medically-relevant information.
References
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Book
A Course in Computational Algebraic Number Theory
TL;DR: The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods.
Book ChapterDOI
Combinatorial Properties of Matrices of Zeros and Ones
TL;DR: In this paper, a matrix A of m rows and n columns, all of whose entries are 0's and 1's, is considered, and the sum of row i of A is denoted by r i (i = 1,..., m) and sum of column n of A are denoted as s i (1, n, n).
Book
Discrete tomography : foundations, algorithms, and applications
Gabor T. Herman,Attila Kuba +1 more
TL;DR: In this paper, Kuba, Gabor T. Herman, Eilat Vardi, and Cun-Hui Zhang present an algebraic solution for Discrete Tomography.
Book
Polynomials with Special Regard to Reducibility
TL;DR: In this paper, most of the known results on reducibility of polynomials over arbitrary fields, algebraically closed fields, and finitely generated fields are presented, including results valid only over finite fields, local fields, or rational fields.
Journal ArticleDOI
Discrete tomography: Determination of finite sets by X-rays
TL;DR: It is proved that there are four prescribed lattice directions such that convex subsets of En (i.e., finite subsets F with F = En n conv F) are determined, among all such sets, by their X-rays in these directions.