Variational reconstruction with DC-programming

Applied and Numerical Harmonic Analysis

Volumn , Issue 9780817636142, 2007, Pages 227-243

  Schnorr C ^a   Schule T ^a   Weber, S ^a  

^a UNIVERSITY OF MANNHEIM   (Germany)

Author keywords

Binary constraint; Discrete tomography; Iterative reconstruction algorithm; Quadratic optimization problem; Vessel system

Indexed keywords

EID: 70449349475     PISSN: 22965009     EISSN: 22965017     Source Type: Book Series    
DOI: 10.1007/978-0-8176-4543-4_11     Document Type: Chapter

References (26)

1. Baumeister, J.: Stable Solution of Inverse Problems. F. Vieweg & Sohn, Braun-schweig/Wiesbaden, Germany (1987).
2. Bauschke, H.H., Borwein, J.M.: On projection algorithms for solving convex feasibility problems. SIAM Review, 38, 367–426 (1996).
3. Beck, A., Teboulle, M.: Global optimality conditions for quadratic optimization problems with binary constraints. SIAM J. Optimiz., 11, 179–188 (2000).
4. Birgin, E.G., Martínez, J.M., Raydan, M.: Algorithm 813: SPG-software for convex-constrained optimization. ACM Trans. Math. Softw., 27, 340–349 (2001).
5. Censor, Y., Zenios, S.A.: Parallel Optimization: Theory, Algorithms, and Applications. Oxford Univ. Press, New York, NY (1998).
6. Demoment, G.: Image reconstruction and restoration: Overview of common estimation structures and problems. IEEE Trans. Acoustics, Speech, Signal Proc., 37, 2024–2036 (1989).
7. Engl, H.W., Hanke, M., Neubauer, A.: Regularization of Inverse Problems. Kluwer, Dordrecht, The Netherlands (1996).
8. Floudas, C.A., Visweswaran, V.: Quadratic optimization. In: Horst, R., Pardalos, R.M. (eds.): Handbook of Global Optimization, Kluwer Acad. Publ., Dordrecht, The Netherlands, pp. 217–269 (1995).
9. Giannessi, F., Niccolucci, F.: Connections between nonlinear and integer programming problems. In Symposia Mathematica, Vol. 19, Academic Press, Orlando, FL, pp. 161–176 (1976).
10. Golub, G.H., van Loan, C.F.: Matrix Computations, 3rd ed., Johns Hopkins Univ. Press, Baltimore, MD (1997).
11. Gordon, R., Bender, R., Herman, G.T.: Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and x-ray photography. J. Theor. Biol., 29, 471–481 (1970).
12. Hackbusch, W.: Iterative Solution of Large Sparse Systems of Equations. Springer, Berlin, Germany (1993).
13. Herman, G.T.: Mathematical Methods in Tomography. Springer, Berlin, Germany (1992).
14. Herman, G.T., Kuba, A. (eds.): Discrete Tomography: Foundations, Algorithms, and Applications. Birkhäuser, Boston, MA (1999).
15. Herman, G.T., Kuba, A.: Discrete tomography in medical imaging. Proc. IEEE, 91, 1612–1626 (2003).
16. Horst, R., Tuy, H.: Global Optimization: Deterministic Approaches, 3rd ed., Springer, Berlin, Germany (1996).
17. Kaczmarz, S.: Angenäherte Auflösung von Systemen linearer Gleichungen. Bull. Acad. Polon. Sci. et Let. A, pp. 355–357 (1937).
18. McLachlan, G.J., Krishnan, T.: The EM Algorithm and Extensions. Wiley, New York, NY (1996).
19. Pham Dinh, T., Elbernoussi, S.: Duality in d.c. (difference of convex functions) optimization subgradient methods. In: Hoffmann, K.-H., Hiriart-Urruty, J.-B., Lemarechal, C., Zowe, J. (eds.), Trends in Mathematical Optimization, Birkäuser, Basel, Switzerland, pp. 277–293 (1988).
20. Pham Dinh, T., Hoai An, L.T.: A D.C. optimization algorithm for solving the trust-region subproblem. SIAM J. Optim., 8, 476–505 (1998).
21. Popa, C., Zdunek, R.: Kaczmarz extended algorithm for tomographic image reconstruction from limited data. Math. Comput. Simul., 65, 579–598 (2004).
22. Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Springer, Berlin, Germany (1998).
23. Schüle, T., Schnörr, C., Weber, S., Hornegger, J.: Discrete tomography by convex-concave regularization and D.C. programming. Discr. Appl. Math., 151, 229–243 (2005).
24. Schüle, T., Weber, S., Schnörr, C.: Adaptive reconstruction of discrete-valued objects from few projections. Electr. Notes Discr. Math., 20, 365–384 (2005).
25. Vogel, C.R.: Computational Methods for Inverse Problems. SIAM, Philadelphia, PA (2002).
26. S. Weber, Schüle, T., Schnörr, C., Kuba, A.: Binary tomography with deblur-ring. In: Reulke, R., Eckardt, U., Flach, B., Knauer, U., Polthier, K. (eds.), Combinatorial Image Analysis. Springer, Berlin, Germany, pp. 375–388 (2006).