Discrete tomography by convex-concave regularization and D.C. programming

Discrete Applied Mathematics

Volumn 151, Issue 1-3, 2005, Pages 229-243

  Schule T ^a,c   Schnorr C ^a   Weber, S ^a   Hornegger, J ^b  

^a UNIVERSITY OF MANNHEIM   (Germany)

^b UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

^c SIEMENS AG   (Germany)

Author keywords

Combinatorial optimization; Concave minimization; D.C. programming; Discrete tomography

Indexed keywords

ALGORITHMS; IMAGE RECONSTRUCTION; OPTIMIZATION; PROBLEM SOLVING;

COMBINATORIAL OPTIMIZATION; CONCAVE MINIMIZATION; D.C. PROGRAMMING; DISCRETE TOMOGRAPHY;

TOMOGRAPHY;

EID: 24944589921     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2005.02.028     Document Type: Conference Paper

References (21)

1. D.P. Bertsekas On the Goldstein-Levitin-Polyak gradient projection method IEEE Trans. Automat. Control 21 2 1976 174 184
2. Y. Censor Binary steering in discrete tomography reconstruction with sequential and simultaneous iterative algorithms Linear Algebra Appl. 339 2001 111 124
3. M.T. Chan, G.T. Herman, and E. Levitan Bayesian image reconstruction using image-modeling gibbs priors Internat. J. Imag. System Technol. 9 1998 85 98
4. G. Demoment Image reconstruction and restoration overview of common estimation structures and problems IEEE Trans. on Acoust. Speech Signal Process. 37 12 1989 2024 2036
5. P. Fishburn, P. Schwander, L. Shepp, and R. Vanderbei The discrete radon transform and its approximate inversion via linear programming Discrete Appl. Math. 75 1997 39 61
6. T. Frese, C.A. Bouman, and K. Sauer Multiscale Bayesian methods for discrete tomography G.T. Herman A. Kuba Discrete Tomography 1999 Birkhäuser Basel 237 267
7. R.J. Gardner, and P. Gritzmann Discrete tomography determination of finite sets by X-rays Trans. Amer. Math. Soc. 349 6 1997 2271 2295
8. F. Giannessi, and F. Niccolucci Connections between nonlinear and integer programming problems Symposia Mathematica 1976 Istituto Nazionale di Alta Mathematica 161 176
9. G.H. Golub, and C.F. VanLoan Matrix Computations third ed. 1997 Johns Hopkins University Press Baltimore, MD
10. P. Gritzmann, D. Prangenberg, S. de Vries, and M. Wiegelmann Success and failure of certain reconstruction and uniqueness algorithms in discrete tomography Internat. J. Imag. System Technol. 9 1998 101 109
11. P. Gritzmann, S. de Vries, and M. Wiegelmann Approximating binary images from discrete X-rays SIAM J. Optim. 11 2 2000 522 546
12. G. Herman, A. Kuba (Eds.), Discrete Tomography: Foundations, Algorithms, and Applications, Birkhäuser, Boston, 1999.
13. R. Horst, and H. Tuy Global Optimization Deterministic Approaches third ed. 1996 Springer Berlin
14. A. Kuba, and G.T. Herman Discrete tomography a historical overview G.T. Herman A. Kuba Discrete Tomography 1999 Birkhäuser Boston 3 34
15. S. Matej, G.T. Herman, and A. Vardi Binary tomography on the hexagonal grid using gibbs priors Internat. J. Imag. System Technol. 9 1998 126 131
16. F. Natterer, and F. Wübbeling Mathematical Methods in Image Reconstruction 2001 SIAM Philadelphia, PA
17. T. Pham Dinh, S. Elbernoussi, Duality in d.c. (difference of convex functions) optimization, subgradient methods, in: Trends in Mathematical Optimization, vol. 84, International Series of Numerical Mathematics, Birkhäuser, Basel, 1988, pp. 277-293.
18. T. Pham Dinh, and L.T. Hoai An A d.c. optimization algorithm for solving the trust-region subproblem SIAM J. Optim. 8 2 1998 476 505
19. R.T. Rockafellar Convex Analysis second ed. 1972 Princeton University Press Princeton, NJ
20. S. Weber, C. Schnörr, J. Hornegger, A linear programming relaxation for binary tomography with smoothness priors, in: Proceedings of International Workshop on Combinatorial Image Analysis (IWCIA'03), Palermo, Italy, May 14-16, 2003.
21. S. Weber, T. Schüle, C. Schnörr, and J. Hornegger A linear programming approach to limited angle 3D reconstruction from DSA projections Methods of Information in Medicine 43 2004 320 326