Discrete tomography by convex-concave regularization and D.C. programming
Thomas Schüle,Christoph Schnörr,Stefan Weber,Joachim Hornegger +3 more
- Vol. 151, Iss: 1, pp 229-243
TLDR
A novel approach to the tomographic reconstruction of binary objects from few projection directions within a limited range of angles with robustness against local minima and excellent reconstruction performance using five projections within a range of 90^@?Abstract:
We present a novel approach to the tomographic reconstruction of binary objects from few projection directions within a limited range of angles. A quadratic objective functional over binary variables comprising the squared projection error and a prior penalizing non-homogeneous regions, is supplemented with a concave functional enforcing binary solutions. Application of a primal-dual subgradient algorithm to a suitable decomposition of the objective functional into the difference of two convex functions leads to an algorithm which provably converges with parallel updates to binary solutions. Numerical results demonstrate robustness against local minima and excellent reconstruction performance using five projections within a range of 90^@?. Our approach is applicable to quite general objective functions over binary variables with constraints and thus applicable to a wide range of problems within and beyond the field of discrete tomography.read more
Citations
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ReportDOI
Discrete Applied Mathematics
TL;DR: Significant progress has been made with solution of location problems and in preprocessing and decomposition for discrete optimization and on the application of techniques from combinational optimization to nonlinear problems.
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
DC programming and DCA: thirty years of developments
Hoai An Le Thi,Tao Pham Dinh +1 more
TL;DR: A short survey on thirty years of developments of DC (Difference of Convex functions) programming and DCA (DC Algorithms) which constitute the backbone of nonconvex programming and global optimization.
Journal ArticleDOI
A new efficient algorithm based on DC programming and DCA for clustering
TL;DR: A fast and robust algorithm based on DC (Difference of Convex functions) programming and DC Algorithms (DCA) is investigated and preliminary numerical solutions show the efficiency and the superiority of the appropriate DCA with respect to the standard K-means algorithm.
References
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Book
Global Optimization: Deterministic Approaches
Reiner Horst,Tuy Hoang +1 more
TL;DR: This study develops a unifying approach to constrained global optimization that provides insight into the underlying concepts and properties of diverse techniques recently proposed to solve a wide variety of problems encountered in the decision sciences, engineering, operations research and other disciplines.
Mathematical methods in image reconstruction
Frank Natterer,Frank Wübbeling +1 more
TL;DR: This chapter discusses reconstruction algorithms, stability and resolution in tomography, and problems that have peculiarities in relation to nonlinear tomography.
Book
Mathematical Methods in Image Reconstruction
Frank Natterer,Frank Wübbeling +1 more
TL;DR: In this article, the authors present a reconstruction algorithm for nonlinear tomography problems that have peculiarities, based on integral geometry and structural and resolution properties of the tomography images.